Full text of "KAPREKAR MATHEMATICIAN - MARATHI"

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VxX, H X fe#W,RfeR, 3fe|R, fefe fe# 3TW 3nf?RfR 


nfRRTRRt Rnfen 


V9V9V9 X = FFF x V9T9 

x W = W'lfV x FFF 

W X ^\3^T3 = ^V9^V9^V9^V9 x 

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RROT RRRsT RJlfer : RtRR nftRR ^ 



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wk 


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5^0 T^» RIT RTT^T RT?tR. “iNalddl 

t 3< l ^lHd T IR fWW ^RTTR 37T%- 

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Rl^R HR RR'RlfHRRT 3TNRTT ?RTRT ^?R RTRT 3T[t? 


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=blfl Md 


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?T f^RTRi =hl« u< Hl , wl6l R>IH<=b<idl Rft M Rd) M? eft 3TRTt : 


?T f^RTRi =hl« u< Hl'Wl6l R>IH<=b<idl Rft M Rdl 3Rt eft 3TRTt : 
cfluidt ft rfR3TR5t WTT Mr '3dR RiR dRldldil (ftRRf RRRRRTR 

Mr)' MM w* it f&m r^rt Mt. w wyx rtwt 

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RRsRT Merdl eRt Rleddiei. 

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3RTRT Pdfgdt RTfMt. RR eft 3dR RTRTR RRTR *ft rM RTsRT f*M eft 
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RRRt ? : ehWifllfl RR Mft RTsRT ^RT. 


RTRtt l 
RTRtt R 

rtM 3 


RTRTR eft feTRT. 


WTT 3TRTT RTRTR RT5T. 



3^T. 3 : #T sNi FFTR 


R ^ 3T3J f«Rr 

f^ejt^sqr 

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^ ? : 3V<^ 3eR^r sfRR fc^T 

4I ^ v : W3-3V<:^ ^ STTf&T 3 JFJp WlMl <MM|cb). 

= 53 V* 


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e *^ 1 '^ dHId ^ Jf^p ft ^fpf TffipTT 

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^H^id 3iicrlci) TRs^IT 

cbiflH 

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r o^va^ 

^VS^o-o^Va^ = 






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3?r. ^ ara> *ptr 


3fl?TT 1 EtT> <=b)gch ^HM-d ^ T rf^Trf =F^. 


r; ^ u -r: .. 

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JTT^T 

C*1HH 

fafjT 


KHdl Tchcll ^)qcr*4[ 
3ii^dl 


6\3\3U, 

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= V9 


\3\B^l 

??V9\9 

V9to??-^toto= 




= ?o^to 


6^o 

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4^?o-o?toi = 



W\6 



f8j, $ *V3* fT ff f&m ^ficqr W&T frioSlcTr. 


T Tf&ldM<l chmlcbi 


% 

R 

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cht^H 

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fci^iw an^tt hwi 

5bHl4 

tFfT 

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w 

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^0 

°w 




w*. 

= t- 0 ^ 

C°CR 

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o^66 

66^o-o^C6 = 

tw 

6^1 


6\^R-RV \C = W* 


fsf, UMoOT MN'flcT ^ f^<i+ ^cTt. 


3T«IRT : 3TTcTT midKTBt ^ o o ft cfc?t 3T3T c^^<| SFT^fcft 
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3^T. * : f^Hi* ^'sX ft Relc-fl uwl $35 


^to* 


toW 




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TJgjTET ^FRtcT M. 

fa ftspi : rfFft ppT ^ISWTcT TfaZ^TT WTRT ^TT <*>*H 
sn^eft wtt Iww =byV1df swt. 

FIT JTFfai y^tdT ^ ^TFT "dial. 

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5t,HdK ^FT ^RTcftcT FT R^<i ( + mf$HM Mi^dcil fFSTTt. 


3^r. ^ 







= ^^V3V 




^‘a? 

^m'n<i-an TTfTncft HJi-O-df 

° ^ 

= ^V9X 
U 



^ Wtcf ftRTRf fto6U<!JWI6t TOtTOdl 3 PUsf)d 
fRTO RTfllddl 3TT%. 

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^ ^ TOR WT S>, V ?; o, *, X 3TT^ cR T£5T 

TOtcT tt. 


' 3 Hl**fl 2 fp 


3TRT Ib^ch i 


3^T. ^ : ^*35 ft WTT W? 3T?ft: 


3ft RT 
ftrT t - 


= 3 ; $-Y = 3 ; Y -3 = * 


3 > •? ) ? f 3 TRR 4 H=b tdTcf. tq?T Rfi? R TOT 






W^YS^ = 5 *V 9 Y 


3^T. ? : 6<a^3 ^ WTT 6^? 3T?ft 3d<cR 
<i -^9 = l; V 9 -^ = 3 ; ^ 

Wti ?R TOR TO S’, 3 tm ft^T 






^ ^l 3 Y 


ff^o 1 TOTRTT! 

RTTORl%tRt Y, ^ O anf&T o, Y tTORftRTRTTOR 

TOrort ttst tro 3 rtr rrt tor! ftRRF tdt. 

■^T- 3 • 3 R 3 ^ ft t<sqi 3 d<rdl TOM % <a $ 3 3 Rft RTS - . JR 


TO. 3 


VR = Y; R-? = a-? = o TOR 

*> 3, 0 I TOR TOR tdR. tq?T 


3R3^ <^R33 


33R<; 


^R 33 -? 3 R^ = ^V 9 Y 


RFft Y^ott RRcT! ^<ie1 3RJR ^RH RTTeft sRKR- 
$(le)<rqi R.RT.dR'idld MRq^d rdidl t RRld JRR 
^T Y^O 3TTf&T $^V9Y aifqehKct,. RMiddl Rj fojHI 


chlWVM 


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Tfj t^ fT ^TFT *fpft 'rMM’d< 3* d^Ml 3#)^Mld Y^ott ?t TOR 
3 fl 3 ^jT SffcrfNt l^cbtcbi^t =b<*f“ifh ^T 3 RRT! 

33T. Y : ft tf^TT 3?R^TT shHld tt. 

t 5 ST, = °; ^ 3T1 ^ rT ^ = * 

T ? ,I f^, 0 , ^ , Y t 3fTcR TOi faasdld. 


^66 66 ^ 
3RT, 


d 3rR tf. 


66^-W6 = ^^V9Y 


3f^f J^cTRT 3||(rlcrdl Sf^fdKjd Sflfnj ddi-oHldf. 

TJyPJcf ^f&Tcft f^RTT «b<dHI ft^Tlt ^JcTFjcT 3#T ^cfMt ft 11 !^^ H<qd 
RI^T, 3jehJ | [uid1q STRFffte TO '5fcT^ WI 'TOt *fp£T, TOf^TOft 
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cf^M (U 3RR ^ ^ld 

%^fT. 

cdl't'bl °blfl <ldl Ml^: 

%) Tjti Wft <a 3 fRUIMI tW# ^f 

?t d^t cf sRTRT vjjufpTT SfidN^d nRFdd $fleleit 3TT%. RFJT TO 
t^TOTOT cTOTT Fft TO'. 

3<l^<TO gf , ^ «aTO 3fft. cTOfBt H^fT TOR 3d<ldel 

f 3TR5 tfoSRr. RcR WTOeRT 3RT cRTW ^H 
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3fTRvgT ^^ : cRT RPT 6dl ^ u l^ 

(^)’ = (?x y) (\y= uva 

3RTT Rt RRTO RfaJdt. 


j if u rcft ^ttNt 



Jraft, 

u^y = Uxv w = 

(%°^y = (?o x %\) (^y = 

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= (^ Vx 3 00 ) (< 0 * = E^Vsoo^ 

3T^ ICTE- cjrf ifarcT. 

^ ^ 4fact, fogflT ^cTRT ^rq^TRt 5?f WE^TT 3RE x TTH^TRT 

rft y'oHI ( \ o x + i\) ^ 3^f 3^ ^ ^ 

(?°x + ^y = ^o x ( x + ^) + ^t A 
3RTT feWR %^I=K 

= (*o x 3 + < 0 * = ^oo x ? + ? ) + ^ 

= + ^ = 

^ ^ ^"S^ti 06 , ficffa ^5?f ^IR^T 3T3iM ^stef a ^dK 

^T^RTt diT J j u liq>K cbiJ’H-cil, ^ 37Ffc^JT HTHId ^?f. 

*) ^ WRTrftH 3T3> mR «T Tt£ W T-t^l 3Tgdrft * o 

3W WsilWF T p i l^K - 

m X ax^, \3\ x ?c^Tt WfT%. 

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■Wumcdl ■Hhm 3jct,|-c|| i^colci sbnqK qfe^fl"yiTl^R 

dv^d ^|^ef| >Hot|| feT^r. 


35 f. $ : ^?x^ 


^ WH^I 3 raM 
E?f ? ut 

5®^T Pb^qK ^Rsi) 


3 x V3 = H 
3 x 3 = 5 


3 ET. ^ : EVx<£^=(£x^)(Xx^) = 


* x % = % 

V3 X E = 


3^T. 3 : x 

T& ^TFM JJ,u||cbR 
V9rrr 6 ^T ^StcT 
fFRRTR tiAft J jU||^R 

TRT °RtcT MR, x ^9% = I 3tR ^R 3# dtf? 

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%cff dR, 3HHC"HIQll 3TNeft qia^ ^ef. 

\3o x Co = <^oo, 3TOT ^R 3TFF5t J JU|ld>l< ^dt. 

srafdd x axu^l 'tf a<iq>sl 3RRT mis'll. rqiq< aniq 

TfflJE ^ **IHMI JpileRR 

* x ^ ^ 3RTT R §dT dt O ^ ^If Sfitmzi ant. 

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O^ SJTM. 

^T M^fT f^RTK ^TT^fT afe aM Y 11 ^ ^T 

%M. : 

3 ^T. >£: ^'Kx^^=( 3 U ; !?)^xO = l \^^ 

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331 . « : : J^^ = ( 3 ^U? 0 <) 0 )( : )x^)= 6 %%^ooo%^ 

cR ^ 4 |-ci|| clanai* TtxTH ^ftcT 'Jidlqi HSdlcxJI 

EhT : f«T^5T, (3? +W) (3T +^S), M ^ + ^5 = ^o 
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to m 4 l ■M'HH 3 Ri a tomHI^HI 3 ^rat Mil'll \ o 3 iyu||'-q| c^iH 

*?tot, il« aiato tola % o an# tot, ^ ^ ftoar ant. 


*R|FsK H 3 T^J 3 RTUfMI rjtetol at ato ^t aia T^nrt, 

to mam amat toto *o anfa tomat ata ato 3Rmm to 
Mf (aRja: ^ tom ipreHjqcF ato to^T^T ^u||c|,K ant, t 
m 41 4141 a*ja %tot ant. 


m4l4) a <*mto< nfat anam chitonal nRara toat 
to 4) ant. tomaim 41 =h ^itoi ans atotw an 7 ! rrt arcm at 
attofl TO 5 TO WtTTT. t^T nT 3 TO JpItolMl tot to ?n 4 t ttat 
an? ^IT^TRt malm ■cbwfiJH 3 T 8 M t TOrftoa 
ar4t ife fntonr mm ‘ton nfta’ tonamr Rjto tot tot 
an? art antt am aaaTa. w t a^toa win? 


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H,u||cbK 

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to : WT V3H X anaa TOP?!. 

to, w wm to atom ato tonaft 

3 x 3 = $ arm ^nanr anm, antot $, ^vsvmnpifdtot. 
- 

m. * : RVsh x 

m. ^ : £V3 <a x = (a ^)(V3H x RH)= 
m. 3 : U^XU^ = (UX^)(«HX^)= 
aan. * : x = Uu x vso o ) (v3t\ x }h) = 

tt to aim IfTMt. «FTWr V 9 ^+ 34 = \ °o. 

ar?to %°o 4<4al, a a vs x 3^3 ato 41 si 4 a 41 to m ^w 
j^ii^k anar to. 




nfdarnt mton 


(W x 3^3) = (3 X *) (?VS x U) •/ 3 VS + 

= = ^°° 

m, ?V9 x s ,3 jjuiicbn ftorg' 3m wto 
to: torn wpfrtt tt to wto to ^ftr to. 

^) to feT toto isf ato nig V9, c, to to tom 
toi4 to 

war4, ^vs, V3<:, ^°V3, u^, 3mtto^?n 

4dld. 

to: WT to mtot ^T. ftolddl to FIRM 

to fto tor WRM cT^TTcT to (to 3 RT, to to) 
xrt m to mRcfi to i^to 
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toiHi j i fto. mcf anton ?im, to mam 
3iwi gto ^mR 4to^l ^uiicbK aJTO anton 
arRirr tom. m jjuiichR toctor ftoton to 
atom to (totto) fto. to : 

to. % : (^to 

toton 

mto ^ : to ma vs^t to mto 

(vsy* = x<^, tot ^ fto 0) ^ 

arto 3 : to mat ^ ma ^ tos^ aiam x ?T?rma to 
U + %) * = * 6 , tot 6 tto('i) ^ 
aitot a : toat to mat to atoa *h=)k tom vs 

.*. ^ X V9 = 

ma artot ^ ator, * wiaar fto^. 

/. 3 = ** (iii) 

maT, (i),(ii),(iii) in atota^a si 41 to fd^a aar ana. 
(^y = 

aaq^r aaaro m. 

aPnat aatoT tor^r ^ 



3^r. * : (R^)\ ^R5T 3fa 

V*. = % fef^(i) d fRRT 

^ t hfr) wit 

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^t, m x 3°) + *V= W (Hi) 

STRT, (i), (ii), (iii) phHlci dqqlqi^q siq1q>s ferfi|jT, 

(^^%y = W°*, t 3 tR ftaa. 

3^T. } : (<*<><:)», 3 3Rt WIT 

H U)’ = 5*, ^ fa^(i), $ ?TeRT 
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— (<A° + Ox? = K ^ ferfi? (ii), 3° T?TeRT 
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3TRIT, (i), (ii), (iii) sBhm -iqqlqvsq 4lq1q>s ldfBr4l e H, 
(Ho cy = ^H 6o^, | 33R. 

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t^THFT 33FT %cft. 

m , 

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WIT 3^ H faHRT. 

3'<lg<u|l4, ^°V3H^3<i 

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/. 3 ^ 'T HR 'Jiiell. 

3^> H HR 4|U||R| WIT 3i)aMs|Ui|Hl $ 3Rl7f 3#. 


3*3 H HR 


^) fa^lerR H^?IR ctf WT ^ ?fa5T fa^RT <RH (3T) R H#T 
(^) 3 R#3 qpbqieo RR 'bi<o u i. 

TteT : (3T) RR ^TRT Jpf 3R. HT H'lfHHi fcelxrHI' Rl*1< 
^ccr: <r=r fcT^T. ^ WTTHTH ^?IRT ffa? 3T. 

I ^ wrrt 3 3Hf3 SIR Jfef. HT RMlerll fa 
xj^TR yHT. HR^f ffeeT y^erlM 3 Wh R^RTTS 
fHoSef. 

3^r. ^.m^/?t. ^ ^cr h ° 0 wir 3 Ha>qi<a RR ' 


^TRf cbT^f. 


WKt ^ 
Wirt ^ 
writ 3 
HFRt V 


^IRT (^)’ = 3^ 

^TJcft 5>H<i ^ x ^ ^ 

^ WIR 3 = .^3^ oHW 

H o o WTR ^ = H°°xo.^^ 

qq)cqi<o sn^l =:%%.6 o 


<Tfa : A = P(uH n ^^A = H0»(u-y 


^ \^T 


^T=^ (^ + ^r) 


= H00 X ( ^. 0 

= H°o x 
= H^^.d 


. SIR = A - P 

• • 

= H - ^A 00 
= $\.6 

(«T) 3 TOR SIR : 

fteT : ^TRT M ^TRT ^TfcTT 3^ ^TT- RHeK 

RR ^TRT 3^T "yR. ’JIT H'looHI tm ^TR 
d^jlcB^ T ^lefl ' ^ g 3T?TT fa?T ^ft, RRt T& RR 
cHRl 3Tlo5teTRIT feRRT 3fan3Tcft teller!. lel^NI 

^faeT 4Ml=H5 ffa? ^T- t * 

*><!HR 3 ' ?5 RRR sir. Hlerli H,^enM ^Piel 

^?t f¥ ^*4T5 sir ft55^. 





3<is< u l|2f, H°° X dTFT 3 ddfd sqi^r dddT. 

Fd% \ : = (vy = o^ 

3 : 3 (°<HI'Jlc;<) ;? = 3 (*) ? = ox<i 
^Mil 3 : 3 (MlddO = 3 x X = X^ 

•4 Ml %%d : o ^ x 

o ^6 

X l 

X ? V C ^ X 

dT Hid <*l%| ^<jh \ 7> H d I d 
3 ddfd ’ddMId cZJT^r = .X'WLSC* 

.*. H 00 X% WT =Hoo x 

3 ddfd -c|pbc||<s 

• ^Kdl %Oqi 

^l 5^ ^TTWgdT, STTddtcff Ricii fqHMmi«sHI Sldl%) dlfdTd 
'dFedlW 37*JW£T 37TqedT dMHId %dJd. W 

dT%fT 37TWT WdT 37fdd7 dfTd 7%T dlft. TTRTT 3RJT 

^T^FTT dFd 7% fddl, fdidl dl<3H u l] cdT STdcdTcTT ft dddT fdflldd' 
<lHN=hl(l dldcl. -^Krll %7sdidl dTtd ft 3T?ttM <ldidd>kdi 371%. 
3FdT \ Fctt %dW %ffdddl-ifdf ddWId %^T d% 3 7 1 HHI%lw 
■S’Mid dilH<d><i'cdl dT Hommi ^iell! *f>up 'cdiw'dlddl TJdT 
3TFTo5 ddld 37%. 

^’<9HM 3^ ftdd dddIMI dimtdRM fH d d l d l d 37MM || ^)% 
5^tH» ddT%t Id did ^rdi%q<l<n %7°did>4 cl^T %% WT cTFT 

-FcT. 3R7, 7JSFT Pull'd di<. u di-cqi d J ii4 J ioodi dKI^Hd, f^TT 

^d's'sY, 37dTT d4ddl Pklcodl 7pidd%dl 

WsF cdTW Sloodi^' 3*dT dffddT. ^jj «n d)w %7°%d #f^T 
^Ft, ^ldld)sq 3ddld)4 5fmRT fdW 37d5T%, 3TdT (l), WIT (M) 
37T%T d'ddl (r) 37% %% 'HZ HlSdl 4dld. 


otiiisqi : ^5dT %7<%W 37diT% L, M, R 7? did stdFJ 37% H-Sdld 
%t, 5TW dldddl d3 L 37lf^T 3RW dld>MI d3 R dTdt %%d (L + R) 
4icd Td7 d lid 17 %FI7T 3%F, M dT ddW dSTd 3R7dt, fdoTT dk% 
% 7 W TfFdTcT. 


d%teT 3<|^<u|id7FF ft °qi<2dl W? f%ef. 


TO 


L 

R 

M = L + R 

M Htilrl 

clHc(Kc(RHI 



\ 


% = X + H 


* 




^ ^ 



^\3V3V9X 



^ ^ 

dtd^r 





^ - 37 + ^ 


\ 




\\\ = ^\3 + ^ 

dlH^I 

$ 





^pr 

V9 


V3^ 


^ = 0 V97 + HV* 



3%7 : 

\. L M R Mt %%W chTF'H 4 u IKl 37di, M F% R>dl 37f«ld) 4o6| 
%dt fdTdT 3lPsldld WTt *TfT sFT%. 

TRedT M ^TZTTT % D 7I7T 37d7 ^ tdT^T \ %877 %t37 W ^ (d>dl % 
^7T elfH 3R7e7T Hllf%. TTW f7 3fd7 x HlHdl 7R, %^7 tWH', 
X < x ^ ^ , 37% 4Uddld fd'fTd^Hld FScTT %%. 

5. L^ R ^ HIHM'7% TT^IR 3R5 3PFRTF. U7simi4o5t ^IT TRTcT 
TTT5T W 37d7 ^nft 3r77FT rlT cdl'dldl o C?pT) Ifl 
L + R %#57 dRIdt. dfT dF Vs. 

%J<% % 7 sdT% : dT td%F 7 T ^dlfFTIrp MW Wit TJd^f 

37di Slfddi %o5T %35 dTdidt, ^ 37TW HlfJd. 3TdTT %o% %R% %W 
dtlddTd Idlfudiyidl dlidK %F7T7 fT 37d7 UdFTd dRTTd dTcJd cdT 
d>dldl % 7 dt fdTdt %c57 %dt % WR17T 37d7 RrllfUdldl ftdldf 37%. 
dfT : 


7 ° 


■nfoTrllddl 


d) | %d»<i ' g n df&Tdt H'lildl ^^Mid'diT 





N = = * ($), <A, (5), 3T?f 

^VSVSVSX = } (Vs) X, (V 9 ) = V 3 V 9 V 3 

V*S W W = <(X (5= ), W> (^ = 

3*3? = v?x (h) o H, (\)' = ^ 

tiwi^ 3RFTT : t^cTf Wife!' ?3 If^R f^ 

3T(tcT. rmtal 3H4cqicll <*o4d1d 3T?TT 3ilgW) ^ ^ : 

(3T) WIT TC M 3Tf^TcT WIT f3WT fejof WS^cTT 3M 

cTC, fcTcTT RSWRcfeft ti# WTT (qfjPcTfcrt t*# W) ^u i d l d . 

: (i) N = ?X, L= ?, L + R = ?+X = HTpJTL=TR 
^T^TR H ^cSNr %T Rfet 

(ii) N= 3?VS^, L=.^,R=VS^, L + R^^WMR^H 
^T RTijt. 

(w) ^t l ^ r ^Ifet ""kpR srcfefer cNtt ?ft fifet 
Ml (IdfH^H fwiT W) 3j)o4^dl *ITct 

<s^l^<«J|l4, N = (X) ? = XXX, N= (%) = <?<? 

W L, M, R t fd*t?) TC Sifwidld 3RJ*T M W( qi<qn, ^ u 1 1 <1 
3RT 3RRTI foeTT fsTR t*# WIT ('dl4H(l t^f) W) ^uidld. W : 

(i) N = }X WH = :?x (^) ? ^ 

(ii) N= ?X VS\SVS X? = ?X (Vs) X? 

(3) L^ ?, R, ?, — R ? R^T ^ HT#^ *Fl?t 3^, 
^ **>, £> —- 3, 3, ^ 3T% 3eR 3RH ^Tl^ trfcT%^T 3RT R ^ 
3T^T ^ L + M %fe(tjo5 ^fT J^T 3TT^eTT 3RF 3T8lfcRT M 
■^"Hdl, 3RTT ■H^ell 3TT&4q)Kqi ^R?TT (33T tR-lt R5R) ^uidld. 

W : S^XXXXX^* = ?3 3(X)^? 

%RTT WTT g>?ft faaJcldl ^? 

^ <ferMl fefW t#ft fwft WTT WWR ^ qWid) 
RFf <l<aqcn 3Tlt. 

3 3 -iftmi-i<a ^rq^cR 


(S) n Ws^TT, (?°° + ?°* + \° :( + ?° ? — ) 3T^ 

% o% tlFcft^t RTTRi ^5R %^RTT ^T^T '^jf&Te^TRT ^0% ^T^TT tW^. 

■'K^, ?0‘+ ^o' + ^ o’ + ^0 } — = (^ + ^0 + ^00 + (OOD + -) 

= UU- 

■qRT 3T?f N cTT W •HTs^T ^liq-d tcM Slr^i 3Rj (fqidl^l %a5T 
■^nRT) W % 3T^T. 

3^RTT^, ((o 0 + (o' + (o’ + (o ? ) =W(UU) 

%Tt JRM ?T JJUlIcbK W 

^V9^o 
^VS^oo 
^ o o o 


few, ^o^^ = ->,o («^)^ f tWTt WTTfW^. 


J Ju|ld>K R ^ ^ 

vJddldi^H ^ \3 ^ 

3fefei3 ^ vs ^ 

^ vs <> 


^ Vs ^ 3Wfe^T 
^ vs % 3^wfe)3 

^ vs ^ 

V? vs s 




3TR 3WTT 3Ttf?RT ^IldiK R^T - TfF*fet Scfe? ^33TT 

3Tto5fe fdi?l<VHI ^Vs<^ cTWTT 3McT Mf^RTT ^IT TJ^ W, 

siqlqis y<qi'|H fci^Ndl — cqiq] %fejf q^d ^WTt ■H^sql eft 
fdcbo fe (3H^HdH^H) f^RT ^kilch^i (twr^FT) tfefe ^ , 
sm chmfeR ^UFd TcT. WT WWPf, w fersfeFffeT 3Wt=F3jT 
3V5Rfei# jfe^T cJddl+^T 3WlW3 3T?ft Vilft Iq+ufe Tt#T distil 
clft 3 tR 'fet. 

VR5 ^Vs<^ W§t WIT ^T WI 3TWt 7 Tf^RT 
%fleft cR R %W!T f^T %TR. WT : 


'Wfe+iMl *ll"ld) H'lTldl %T t RWI 


R? 



* 3 3 
* 3 5 

3 X O 
3 X X 


3 3 3 

3 3 5 

3 X o 

3 'A <S 3 V V 


RT t*# WTT RT#fcT. RFT RT 3W3t tffa %# <R, 
^V9ot^^^ + ^^XXs W£35 = <a 3(<0, ^ 3^tr# wit 
, ftcsft. 

3TTRT, % RRR 3IcRMI Rf&mt &StcT ^ ^ sfr.fcRT 

^ qf^TT Mdldc^l W^cT SFfiTdt 3KdM<d ^eT. JRT 
5fflM feufa q&dld t^T ^3FT 3TFT wkr, ^ ^ 


3 5 3 5 

X ^ X H 

<A X <A X 

5 3 ...HlBe^NI vJ<rksMT 5 3 

5 X X £ 5 X ^ o ^ 


RT ^ WIT RT^T. W]- $666$ + XU°3 = 

= WO,XS, ti# WTT. 

3T#R 3RTH 3RRRt 3 aM Wild) RffrffiT &st 


* 3 ^ 

3 3 X 

3 3 3 
x 3 * 

H3 * 


* 3 H 

3 3 X 
3 3 3 

x 3 3 

<\ 3 ? 
\ H * * 0 X l 


Snf&T, + ^U°X^ = V9^V9V9o^ = V9^ (^) ? o^ 

# fi# WTT fWrf. 

(3) f^TRTT oh>|dMI^ '•H^r-ifi X)d>h4l WR STqFiMt 


3i<;clls|<;cl d>^H 3<lctal R^fa ^h’ohi RelHI ■HO^qd %cft 3RTcfT 
#RTt WTT fto5?f. 3<l^<un«f, 

(i) V3£^XH R^Cdl ■HO'HI 
HX3XVS dl=h|-c| 3T3T 

^TT^T U^uT = *(5), ti# WTT 

f v 

(ii) X?<a 53^ f^frft WT 
^V9^^^X3 il e hl , =l ^T 3T3it RZ d<c|H 

^WX = 3^(^) ? ^x, tRTf WTT. 

(3) gafor nfa>a i : f?r cbiur^nf w^% shr dcfaiMi l^tcr 
M^ lcoill^T ebit^Mi t5^T 3T?IRT c#^TT 3FR: fdllcr^lcR, TR^TT 
3i«bNKjH 3TR*T 3R^T IJB W^cT fod% 3Rfi 1%cT^=RT WTT fcT^T TRT 
wM t#5f 3RRTT ti# WTT fw?f. 


3 



3lletl. 


(i) 3 H X 3 
t 3Ri ^55 H'<FTRT 
fel^T WU 

?FIFT ebldc^l 


H X ? 3 
X 3 3 ^ 
3 3 H X 
3 H X 3 


RT Ufe^T, ^HKX= UH), X, f tr# WTT 



3<l^<u| (ji) 

3TRTT | 3T^T ilPd^fc!: %3FT ^FTR 5 

wm\ d.ld(r4l - 
X 3 3 V9 5 <a 

3 3 vs .5 S X 

3 ^ 5 H X 3 

vs 5 K X 5 3 

5 H x ? 3 V9 

V 9 , ff t^# WIT 

3TTeft. 











(*) RRFT 3TR 3RT^eRT ehluMl^l RtR A 3TTf&T B WIT &TRTI. 
RTT^ %, %%, — # !JTR RTRF TRTFT 3FJ3F^ CRD RFJJ. RF 
AxB+BxC +CxD + DxA + A + B+ C + D= ^^... 
RRT. % : ^R A=^, B=^ ?R C=3, D=X • • $cq|<{|. 

.*. AB = ?<A, BC = * O, CD = £ 3#T DA = 

.*. AB + BC + CD + DA + A+B+C+D 

= 3 H + ^° + <: + ^<i + ^+ H + ^ + v= ^^ = (^)^ 

3 ^ 1 . ^ A=^, B =^3 cR C =<SV, D=V 9 $; C,D ^^TJCR 

.*. AxB = 3*7 BxC=UR,CxD= $ 3 <:*, DxA?U^» 

/. AB + BC + CD + DA + A+B+C+D 

= 3 *^ + ^33 + 53 ** + ^Xo+^+^+^y+vs^ 

— = ws = (<0„ 

Rta : ^Rt ^Rlfrft A R B RRtcf 3 RRR^T SIRel^R 
3 RIcf. RfleT 3 RI?FF % to, ARB FR 3 Rfit TR 
RTF! 3 W ^ Rt'Hto 3 Rfnr 3 ^I?RT ^ RKj', A R 
B RfR 3 TRt RHJJF cRT 3 RRR % RR to. RFF# A, 
B^RT 3TRRRstoT to. 

(«0 3TTRRf R5RT9T : N SlfRRRR WIT 3TRRT Rft f%RT to 
3Tf^WI WTTRT Jju||cbK 3RJF TRRRT 3TTRRf RRim oJRRTRRIT (J ) N 
R 3RTRT (*to, -i-x N ) #to WIT ftot. 

R?T : (i) “ = fR, 3 TTRRf RFT 5 >*^Vs 

f?T STTRRf RTFR, %X^6^\9 = ^to<0 o ^V9 3TRT RSRRFR 
ell 41 ^Hrll wtolT <fnHIc 1 felfedl to'. RIFF + ('H'a = 

W % cR f 3 R to RT?t. 

.*. = W(.%) o £«\Vs it RSRRRR cM toit WIT 


3Tlf&T, —x ^ x R 

= SSWS = (S),, 


toll WIT. 


$>\hXm 


(ii) JJ = o.o\a$ ^3, 3TTRRT RTF 

?I 3RR# RFT, = oV^OO. ^3, R^FW 

£to WIT. RIFF, = %%%, RF ^ ^R Rif- 


fto WF. 


U = o\ 3 ^^ x ^ = WW=(^\ 


RT WlfR i -RTR fto R RRRT, -^3Fjn]feR fto 

3TTRRf '<^litols!kR fRFRFf to tolR. RTF RT RfRito, M<N. tRR|FT 
N = R^RT RRRfR STTW 3TFRRFT1 M FBt, M = ^ < N 

3TRIT fRRRt ^3T RTRiRt. F?T : 


sn^eff <vii?T 


o.W'ai'X 




o.HV 3 \^6 
o.\3\^^6^ 




x N ^kiI wmt 

N 

R6<\'9\'* X Vs = =\M^ 

X^ = =*(%)* 

^1^6 X^S = 

X V9 = 'WW'a =^(^) k H 
X V9 = 


J- ...% 3RRRf RFTTFT ^<F% ^RT ^RRIRIRt 
R#R RRTF HIS u flR 3TT%. 3TRTTR ’CldlH 

W 

Vr= to 77= 

3TTpF ^6^ x %'S = = \(%\ t 


RRR 77 = = ovs^, 

?T U+<^ 

3#F 77 x 

\ ? 


= U(< 0 V 



• wit (tW dsrcf) 

S W dRft dddUddl ^t 
edTdt ‘ited! ddT' 3RT dTd f^T. n 
eJHqeldl fdidlFTT *qq?£E| SRTedTR 

dTd ^^XRTcftdt^TarftfTqF 
WT Wqh< ifc§ STfelT fft^RT TdT 


Td^dK WIT ^ThjfT dTRcft fcTelT 
<i^a< eft ‘R-PiRcT i^rft ■Mdr^T 
3 3TFTtJT fcTelT WIT J?JJJ. 

^fichd JR# R fdddd>lfdddd 
TReTF#! dftfdd WdT. 

FT ‘WTTdT fdRT 3R fft 


^FsdT ■dH'Jiuqi'Hidl WT ‘Wdidi fdRT 3Td> ?t 

diaiuj dHq^qq, 3TT%. WIT, '■^■Hldld <=hlu|dl^t ^ifcbl WIT 

N= .(i) 

eR N ^ X, }, Vs 3TdT $3FT 
N # 3Ri = X + 3 + Vs = ^x — (i|) 

(i) d (ii) Wd> ddt WIT, N, = N + feT# 3RT tfNT 

= *3^> + *X = Xd* — (iii) 
*^ u l^ ^didl-cqi N wftwd si^-Od JTfsdtd N, dilddl. 

3T#d N ? d'fF'H 3Td> «k^d N^ dd N d?R N JR N , N — 
H°dl WdT d>l«odl ftefTel. dT dfsh^d dTTdtddiH), ‘3RT 'sft# 
dfdRT’ (IsfadfesH iMr) J^deM 3TT% 3TTf&T 3RF ^fffh^H N 
JTT^T N ? |ft d# WIT Rai^ J^np N •HKOMI, wfteTT, #ddT 3RRT 
<SrMldd) d^sdl ('JH^fd J l ddi)’ JfpTdTd. eR d°dT N TRsftd, ‘dedlldd 
WIT ('ddidS ddT)' J^ldld. dteddld, N^ # dedl<H WIT NSTTftd 
NW dHcSeldl N ? JfTOJd eft eJedlfcd WIT. 3RT diet 3Tlft. 

dfteT <5dl5< u lld, X^Vs eSeMldd) WIT eR Xd^ jft X^Vs 

dT^d dedlftd ^Tfcldl WIT. 

N dT JJS wtdFqd N ?> N ? — fed# d°dT JRTT WIT 
dinsuqidl dflfidT Ridl^l ^Tdl dTc^ 3deTT 'ftit. 

#d : dT d% N JJdM WIT dRprqTdt 3Td 3TT%. UT 
did)^<1d Wcdft^dT RjTRdFT 3dd^ wftdt oqfloqr 
dRdT ^tft. 

SUM : *dT wftelT dft^ldl^l 3edldd> ^ f^feTT 
WIT Jd u ldld. 


cdK94l 





N dTd^ir 


wftdRJd 3dTd fid dl#. ? IR 
dild d^fdl frd^f ?T dft, N 
^Fd T dd W^dte^dl Jdd 


, frfdT 


did dW! 


d, V9, % dTdT =hl u ldl^l < 
WI^ WIT 3TTftd. dT 


qr 3TRdTdRJd fddR %dT ?R, ? , 

WIT dT?t. ^T.dfteT iWTT^TR ddT 
TTdT 3TfddT IdWK ddddRTTdt aTTdd 


n = l %3Td A|u|Mf ddllftd WTTdt ^dt ddd. 

N = ^ /. N^= l + \ = R, = R + R = *, 

N =X+X=£, N^=^+<S = ^, 

= ^ + \ + % =33 "ft'ft WT d°dT WdT- dddd dNd. 
dR $ s(0 fd^ld dHdfqdl ?R, 

S(0= \, 3, V, 4, p, RC, 3 6 ,*%, ^3 — 

?oV 9, — 3Tdft fddft^t HdiM^d eft didddl 


N= 3 dde 
SO) = 3, 


?3, I'a, 3 1, 3X — HV9, iX, — 


Pf ft^pn : S(3)^ J TT drftdT WdT 3 3Rdd fdRT ^1+ STlft. 
% JTTd chl u ledTd WdT JfddT dT?t. 

N= % ^derdld, 

S(^) = U, 3^, 3^ — 

Pl ft s epiT : q^ftqi WdT ^ J]W. 3TWd ^ 0 dt dT ^dtd 
■ftd dT^t, WT tddT dddddT WIT dlft. JpT^ 
l o c ?t WT^ WIT 3dt. 

w d^d^ d ^RTT 3j^dTdTdT m> N ^-dfW 3TdT ; IW dRTeld 
qrftdT JR (3T) ? fdRI ^dl 'Jpid; deeded (d) 3dT dW 3Wfed W 
^dT Hdetd (dT) % JJ^RT 3TdddT, 3RTeT. 3Tdfefd N feddFR fddftft 
ddldt S(N) ^ft ddR dRdT dd. 



3 vmi<* c hi^u' r 

Rei<rqi N *i<s<)dl eh^ll^ai 3TT% ? ^U|-}) eft c^U|^(| Wgihl^H 

fRft? *TT TTCRM RFTfaT ^TRM NW 3 ?TO RTsfclT 
?Tfa ^l-4-cll. 

^WjfT M ^<2^q< 3|cb^<lvj| ijfptvqi N fw 3RT^ cR c*TM 
^RFR N ^ = M 

3TW " . F f S,T Xrri|r?f} ‘ ^rf^TT ^ ' feT^T, TTffrrcft f%F^ff%cT 
^cT fr RW«T qi<ac(c 1 l %ft. 

S(%) 5) u Hdcfl Wll X^ WR virHlRd ^TTefr. RRRT X 1 ^ + X 
+ S = 53 X5 t 53^ 3RTR3T WTT 3#. 




^ 3efR Jrffb^H f[ #f, 53 ^ = X 1 ^, 3RTT 


lell^dl %Tt. WRdln RTR 'ledm, X^ = ?<£, 3 RR, 3 £+ 3 + 4 =X^ 
STm^T RRT 'dl<JH, 3<£_ f = 3 £ ff TTMcodir) TRRR 3R«T 




3 £ art 


3^ ildld WT RTPT RITcR Ididl^l 3RsRT R>l<odl ^tcfTW R>T? RT 
^ ^ 3RJR, 3Rs^TT?Tt 3TRUT 3T WaSd) . ipr# 

firat RcTR'S WTT 3T?m 3RT. RT wleHR RRn| WTT 

R? u ldld. 


^<u||«l, N = 3 5 tdedM< N = 35 = 33 
V 33+3 + 3= 3^ ^ 3 3. ? = 3 o •• ^0 + ^+ 0 = ^ 

^ 3°^ =? f^T 3 ||h u I ajs<3o6dl. RiRR 3°^ ^RR) 3RRT 

3?qi^ WIT diloJdl % RJ?t. ^T 3 o ft WIT 3TT%. TsR ?R 

S(3°) = }o, ^ ? v, *,> ... 

^TT ^ o ft 3TRR WTT 3T^R fcT^lT RFT ^nef % R]ft. 

cl?HRT «5M WTT *PJT ^ ftc^r s$rut 

R^t. fRRfRT % R^R ^ %M S( S> ) M STRUT 

«bi«<^eil ant. 


3TRT % R<R 3 , Vs, % RTFTR^WTT 


7 lfu|dH<l 3Bjq}tR 


x^, ^x, v^^ ) 6$, ^ anfuT 5ioi fcR^TT x ltfcRT ^X 

Wrrat f«f ■ ? rrfcfit ^rr^r wtt n w *TFTt nic^h, s(0, 

S(^) — s(^), s(^o^) ^TT ^cTT 3dld. 

■pTTt^TIT : ^O t %°6 q^EZTT^iWTr %% RRR3RRRZTT 
TrfuTcT ^StcT 3TT%cT. 

m, x °6 + u = u ^ y<s ^ T 

^TRUT, \ = %°\ */ %o 9 > + \ + o + \ = l\%. 

3^y RjfdW (dfq^MNI RRRT ' r f n P TsHtRBt 'JstcT c tilS'+) 
^Ruf ffcRWi cftfT. c*ncT 3^4 SRfeW 1 Tf|^Tr WW 
^o c W^TT WtWIT tcT^fT c^TT 3R%^t RRlT: 3RT nfsb^ 
Iho6 u iiT 1 dcSlRd y<9Hl ^uft felf^cdl 3TT^. 

snfwreuT 4(Mi(^d «<ww1 ^ U H S(N) 

N 

S’ X^ V90 S3S3 ^ 0 ^ ?°3 ^ oV S- 

5 % s;s? ^ ^X ?o a ^ 4X m- 

H ^o \% *V3 ^ 3?. ?V3 VV3 H4 \o%- 

VS ^ Xo YX V\3 ^ 'sa <^a ^X ^ °V9 %X<\... 

% XC ^VS Xt\ HX ^ VS^ C\ %o %<i, ^V9... 

^ o ?X X^ X^ ^vs 40 44 VX X°%- 

IX X? KO HH Vs^ 4^ ?o^ ua W- 

X^ X4 VS4 ^ U* UX- 

^ U 4T ^ ?°a UH- 

S,X VsX 4H ^4 UH- 

vsh 4 vs X 0 * U51 UX U°- 

4^ ^oo ^oVS X U- 

^VS ua *U llt- 

X°C XX^ U^ UH- - 

T<n t ^ RTgn afto 5 T 3 RRrat Chalet 

f«T ^>aV 9 RTeft gr#cRT 'ifuiaft nR^d dJlsWidl d(lci 
R4 |co<hNI fRRR dldell ^Idl. 

a^ 





wnj WIT 3i)aMs|Ui]Ml RRitRt RilRURRJBt ?RTRt 3T#R iJS 
(Isf-ded R^) ft Tfi^efl. 

Hchc^Hl : Rctcrdl N ^Rs^RT 3TRfRt ttt^T RtR 3TRRT cftR 
■ 3ild>s) 3Rcft cR eft RRi Sfaft ft Rftfidl pR ^fT 3^R ^Rst 

Rft RRl 3TR> ij^ol cdldl cRT N ‘aidild p5’ RSU|dld. 

t 3H)d 1J3, f3T5ft d (^t) 3RRIR ^RsMURMI ^f%?f 3TI%. 

RRlfRRT (i) : N= %'S, Rffctt ^ + ^ = ^R STRit 

.*. ^ = V9 

/. d = V9, t ^VsR 3RftR Ijp5. 

(ii) N = 3 W, Rffelt 3 + x+S+<t=3 % ftR 3M 

.’. 53 *^ 3+^=3 

.*. d = ?, t 3WR 3T^njoS. 
d<lf<u| (iii) N = 6^36^6^6663— (R) 
fffett^^r £+d+£+V9+ < '+d+£+<'+<'+i3=v9^, RtR aM 
pt 3fl*r V9 + ^ = ^ fPr arat— fircrct = % + ■$ = x 
tt^T, d=xt (R)R 3RRR }Jo5. 

fcFft 3Rlf<u|ld<rRI d R\ f%Rdt Rl^R d RR PpR fWT %R 
?T^, t ei^fRT tfaf 3MW 3TT%. 

(3T) RT d fRiRT, RR c = - d !, ^ RRR1. 

\ 

(R) RT d RR, RI, c = d d)l<ol. 

c R\ f%RRt RRR N RRT^Rtt Rift, ?t RR1RT %T. RRlRlRt 
N ? = N -er N ? = N - c - N^= N - c - \t, N = N - c - ^,-- 

JpT§faN ? =N -c, N ? = N ( - %, N 5 = N ? - N^= N s - %— ^ISIWdMIdld. 

: N , N,, N - — fR9r|f^Ti^^ 
rdi-41 3Hd,^<lv3) fR5Z*|R Rt RT Retedl N Rt&tfddiT 3TTRT RT fdRKIsf 
3RJeldl N M Rip Rift, ^ fR4I fTR. 1 ■ ; i 

3T ; ; .s : ■ ?-•■ 


f^cft q|R-RT 3HI<=Uf«4<=H ? N Wt fRR% RRi fdddRI HlR-RI d^H 
N TRR*^ =Ft RTft, ^ cJTddl *t?f. 

«k=WM , (Rl) N RtR 3T^t W., N, f N 2 RT ^ RRRTT 

(5) N #T 3T^t cR, Nj, N 2 , N 3 RT #T WRT 
(f) N ^R 3t^t m, N lf N 2 , N 3 , N 4 RT RR RRRTT 

^TT ftcfcT. 

fJT^t, (w) ^grar RRRtcT N 3WU CR, N RW>i Rift. 

(15) c bl u irdl5l Hld<ld N 3lldl dlfl 1R, N 
SRT^TMt -Hlft ft^. 

RflfRR (i) : N = ~66, dlfell ^<1^1 X + 6 = ^tR STdtt 
pRt tftW \ + ^ = 3 , fWT. RIR^R d = ? 
d + \ 3 + % _ 

• C = — r = — ; — = d 

3RRT, N, = N -c ='*6-$ = pX^+X+^=Y<i=N 

n = ^6 RRR^ R^IT RTft, RFRtR 3 tR. 

(ii): N= Rffctt ^ + V + 3 = 6 RR. 

'\d = 6 



3TOT, N, = N -c = RR ^ 6 +^+ 6 =^\ + N 

n 2 =n i - < ^ = = SRlf^T = N 

/_ N= W RRR^WTT Rift. 

(iii) : N = 3 ^ Rff# ^ = * .*. d = 't , RR. 



3TR1T, N, = N -c = 3 STTfnr, + N 

N 2 =N 1 - \ = ^^-^ = ^0 37lfR, ^° + 3 = ^,tN 
^Pft RIR^RRT (N ^RT 3TRRR°RfRRgRT) N Rift. 

/. N = 3 * ft RRR^ ^Rs=R 3Rt. 

<+>tM^. c b<i^RT J lR*ldl H'lOdl 33 



*TRT dcHiqcf) ^TTPTT 3TT%rT. RJT 6'3'X\'$\ 

W Hlftcl 3RT -*mWw1 ^etei 3?]%. FM ^tef 3RtzF STNeRTeTT 
W^TTSf ^tcfT %Tt. cRTR -^- W 3TRdf ^TRTTTT '^U||<1 ft 

ti# WIT SRTRIM 3TTW ^TFpf ^lelef 3Tl|. ^HditsU ft 
WTI^-fil 3TTt, fft cRtcT 3 RtVM f^ FRT ^rf. 

*°> ^oo, ^ooo, * 0 , 000 , * o o , o o o ZJT ^zjr *jf l||dh>RT 
3^TR3I Wm 3TCTRTT <TTt ^00,00,00 i^U|^) ffRT ftf^FT 

t IJR FRJ *fcoSTT 3T^M ^ FFT ^ 3>nU< i^uid l d eft, 
ei^n^T (ftfcFFR) cZJxft WTlcT *TMdl ^iF. 3TR 

R^T ^feqj#?T flRT SHwimteTTefT it 3TT%! 

?faft 3°°*TT ?TcT<*ld<r*TI *^o£, *<**<*, *<*$o, 

3#T *<*<*^ UT sitf^l wfj 
3^c^|-ci c hiH<. c t)<Ml fdNM Wei 3Tlf. TOJ ^TT \%o£ f ^Tel 
WIT Rft! f - 

n= \ %°6 i iffcTt * + < * + o + < ' = \c, fF aFit 
.*. <JTft \ + 6 = % = d, FRT 


3TRT, N,= ^04-^ = %6%%, 

*R U^ + U<^ + U^=U^^N 

^ > N 2 = = uv 

3Tlf&T UV + * + £ + <* + ° = ^o<'=N 

.*. ^o^FRjf ^'IiWn F*JR ^ 3TT%. e*TTttcFft JR^eT 
^fh gsqWei f ^ m frj wit ^fa?i. ^r- ci^Hl 
^isaic6| szjrt. 

3T?M ft#T JTCJT ft^^ER fdilHIH } *czn Vld<*ld, }ooV9, 

1°^, ^oV9\a, ^oC6 3TTftrr 
ft IR ^ WJIM 3TWTM M^dloAl ^cTeTT 3#. 

SRTRTT eT$TR ^{d-c| 3>t RIF ^o<*^ ’iftd-e) 

W<W THU RTR ftcRMI ftfteT ftftcT 3ITfcT. 


Rl>A+{ 


• ft*PT ««4I 

^otjt ^ ^HT ^ 5fe ^ 3IN^IT TT^TRT ^ 

wmt. Wf®n4 <tnU ^r m ^nr 

t^TRt f^teTT ^T M5 ^ c^IM W ' 

fd^lelc^i ^ W?M 'H^W I33>T ^<s^T 

?tcit. 3T?TT WIRT RRT WIT ^fFRR. 

3<I^<H TT4, W 3RI ^51 e!R tW^RTRI 3TFTRTTeTT 
<^Y+ % + ^= ... (i) faoW. 

ft R 3lflRT ^ %# 3|ydl, 

^ + o + 3 = \o\a ... (ii), 'JIT #^T WIT 
T^uit ^ ^ %o-$ ^JT ^IRR f*R 3icb>iqi5MT \ ^TT T^T^T 

yVRft WT IIMT. 


ft Jlf^RT 



Wtt WIT 3TJI e^IRT 


f^rfWTT ^TTTT 

oUlWT : W TF>T W^TT TT^ 8 ^ 
3Tf«R5 3cR^T WTT 3RRTcT, ^ 
' + ° +? F^TT WT WIT *^ u iaid. 

4|N<S'd 3TTWTT T? R8TTTT ^TTef 
3T^f ^5t 'R 3?RfeT ^TTs^TT 
^ ^ R fF 3rMl^ fa'TT 
TFRi 3T«RT y^3eMK=(5 (^T-'JhW^) 


WT WTTRt 3TTRT#T ^Tft 



/'Soi + 'J+oU 



PETT LhiTii'+il 



dTSTTd ^ oo?JT 


wt 3 FJpFT 





U°HU 


^*3 d K%Ro dT Wf 





SVuVa 


d ^°? snfnj d ?<?oh tiPWi^iitr. 

3T?M Jldfe ^?^TT dlddldc) cT^TTd tqfe ^oo^ 3nfwy 
■? ° 3 ? dT ■tt’if^i ^Rs^TT WRMI 3TT%?r. W : 








^ O \^+\3 


^dd^ •H< 2 ^i‘oHi Iq^-cHid 3TFTHT, ?, 3 f V9... 9 i \s ) \o£ ZJJ 
■wq\ Wll 3T^ ^IqjcbST^i ^d%)|ci fdJ^ cdMKI*ik cdT-rdT *dd^ 
Wqiq*H fta»<m-qi 3cqifaT WIMI S(N) dUdddT snf&T 
™ ^ *)fe e l»Kt S(?), S(V9), S(H?) 3nf&T S(X^) dT ^K?t 

^ovs ?r mfa dterc f^ M dtf ^ c friaMl^fo, 

f^RT %edTdT dTldddl WlidfrHd ?oV3 

t WT 3T#dS(X^), S(V9H) JTS^ ?o<* f( WT WIT 

fta^. qP^. 

^td : dfld ?faftd fe%UT %cdld< (?) eh|u|^|^) 

^^WTWIT ?oo^q cI?R^. ( } ) d^T?^ 
dIddTT3I<<kT*ii d dTdfeFT tj^STT VldtfKdfedT cjffif) 
^?T gS^JT ^Tddrtd WFdT Wf WIT fts^RT. 

(?) did W-?<dic;q> WJIddl WF % fdidT ?X %ft 


1 if&Trl I H <1 cfc|i|)ct,< 


3F)d> vJ^Kcfi WdFTHJR TJ^T ^rHlRd WH chl^df ^ dT dddfeT 
ir^i oqrddi JT^T (fddOT 3#q; dddd q>Tf*q^H) dTWddidl' ^o 
STTdRtdT %cT ftd. 

• fsg^ wn 

d^HMUft 3TiquT J|Hdld4d]-'dT J I L MH?I feTi dKdHI HHd, din el, 
WtdT, ¥f, ^ 3T^ dTTWT 7K d(, fddT dTd dTRTdt, dWT 
dTt WTCT, fldT dl J Jdl dTCt, 3# dKd^ R^dddl di J iH dldddl 
?l«g-cj 3dTR dNH <^eqiq< difel^ ^dld ^ STtedJTddT ^c6 <^c6d 
3RT. 3TWd ddIR addlddd 5ldl=hS 3TddT SldldiSd d'JldW dNH 
fl^T #9R %ef 3WcIT f^TRcT d^dd dlft BT?TT W5IT 34-Hdld. 
3<R< RTgf, <a^H, ??*??, ^ 

■UteHHT Ws^TT *^«ldld. FT? ‘^T^ffw Hd4’ RI 

Tf^oodKaidl rdid d u ld 3Tt%. 

tiodi «hi«MqrcD <ld : (?) fdidl^i 3T^?t ^OMI W. 
(^) fd# 3Tdi dFTR fd?T. (?) ^ WTTdt ^<ld dFT. 
(V) it[shdl ^ddd dilslcjaJi %ddldT fa^<a1 'WfT 

dT ^dldl dH# ftT^dT 3T?Tt %^eft dl^t. Rd dt %ddTd^ 

WIT firas^, # d^g^Idt ?nt. dT M^dld dfeRgrfddl ddtldi 3T)dRT 


dT¥d d(. fed dTdt 3Ti)RdR 
felfedlT #dT. 




3ddT dRfer Md 
(^) 5»R? 


dTdft ? 


wi ^ 


fsg# rt 


No, RT^TT 
3 ^ ^ No 4 Cld. sfrHM 

tffer dT5R Rdt WIT N, 
N, 3dIRT did 

^X<? f&?3\ WIT 



4i<h<Ic 1^ fly# WIT faaMdl. 


*TT 3: 

(3) w 



?6\ 9 

No 


^36^. 

No "efr vlddi 3FT 

iJFTTf % 

x°^x 

N, 


%$°x 

N, ^T 3FI2T 

lira# ^ 

\ 0 S* V9o 

N 2 


0 \3^ 0 ^ 

N 2 3d# 

lira# ^ 

x^x 

N 3 


X^6X 

N 3 3d# 

ura# * 


n 4 



N. 3d# 

4 

ura# <c 

$XX°^ 

N 5 

N s 3d# 


xxxnx 

xnxxx 

lira# ^ 


, ftg# WIT 


?^tt w# firar 3(3) * # fly# wit 

ftoJldl. 

(3T) 3TTrTT ^TT 3T3> ^ 3TT%rT 3T9Tt% Mldl'+ *t3d 

tty# WIT 3TdT tdTcT ft ^ : 

X) 

\V= X?X; %V= un 
U Y =W** 

3) UV^STTcIFF 

XXX' = XH*X; XXX* = X^^^X 

3) 

*) ^UU'fT : (UUO ! = 


J iruWH<1 qq qW 


(ar) ^T WlMl tt# 3Wl ^#3 *o#ftdTM ^^A 1 ^,.-- 

^ yjT fty# WIT fncddlci. 

X) XX x S = X^X) XX*XX = X^^X 

XX*XXX= X^X^X', XXxXXXX= X&XXCX 

}) ?6 X S = ^ X XX = 

16 x SSS = WV93; R6 x XXXXX = WXXX^R 

3) x X = V5>V; ^ x XX - *W 
^ x XXXX = WW 
*) V93 x X = W\ ^xXX = WVs 
V93 x XXX - x XXXXXX = 


sirc^rr dspr 3fdd #t ft*# yn^R fly# *i<s#«i<l«K4 £*# 

Ml?t %TTcT. 3IFTI# TJ^ ftfteFT, J j u l-=bld' fdd% X ^TT%T HrRJrr 
3TT#dIT X^ WfT t#H 4#t. 

^ ^ ^ o m^f\ 51d#T ^Ichld^fT 3RTT (3?T ^TKT 3#) WII 
t)^iH ^TT "jidltil h scl l oil ^Idl <Ud. 

tit fly# yfeiiicR ^imWo# ^ k#* 1 3^3 diid 3TracSdF3T 

3>fift J Hcil# 3# %#dt 3H^. ic;i 5 <u||?f, 

(ioo, <^ 00 , ^ 00 , ^nwtdt 3#%#3 3V9 %cT aryr 

eft ?i9 ft:# 1 ! ftWT 3TI%. 

eb)u|d t# WIT %5FT IddMd ##3 ft^T ^*dW“lM # 33# 

tosr 333 y?T fdyr ftffcr %^pr fly# wt ftsff, I siNd t^rt 

WlMT fd^Ndld w?ra 3nt. 

t*dH< u ll4t # ttcT cbN^diCRt ftfW tt^T 3T#t tl'om 

^3Ff fly# WIT faoiduqr# 5#eT ftcT ft# 3#. 

d^luidl# #^T 3H^# WTT 3T# W #t fcTW tNt 3f^F# 

U, X*. - — Xt S3#t ^T- 

#^+4ld, xy # 3T#t WIT HTWTRT, 
x + y = U, t^T f^TT ^ f^T \6 3TT# 


1 % 


Trftrml jpi^i %TO 23ET 



^TR?R, xy,jcy+ 77 , X y+ 7 x 71 , xy + (y-?)^^ ?t 

chl<s l- ^dld # #JTt f# 7 R iff# j)dclld 7 ftg# 

HIT #t. 'v 5 <l^<u||sf J , ^V 9 7 T 7 sIT sfe. 

?I, xy = I VS 37 T# x + y = ^ + Vs = ^ 

3 TTIT, IT# ## g#cT 7 RT# ^eT. 

^VS + 77 , ^Vs + } x 71 , S.VS + 3 X 71 , ^VS +X X 77 , 
^ ^ x II 3 #T I Vs + (y - 7 ) x 77 H 11 # 7 Vs + 7 x 77 , IRUT 

y = VS, giRHUT 3 # 

fwrfR #7 fllT tmH,{U|M‘ f\ at# ; 

7 V 9 
7 7 7 
R 7 7 
? 7 * 

* 5 3 
<\ 7 3 

77 7 

^ 33 /M^vss vs ?t tig# wi. 

^ siqWsn ^qqlqiS £ki)<MU| %?IRT fig# IRsIT #T R#. 
IT fell# #1 g^ cT^TTrT cjqei cR ^IRTT R 3RIT |RTIcT 317 
ITTIIT #T. 7t g^ 3 #, (j) fRI$#eIT ##i (TRTRIH - 7 ) ^TTUT 
t##RTT WIT 3 tRRTT# g#T #TTI. (ii) TgfRIHIT 3# 3rRRIT 
## dlcbldl #Tt. (iii) IRIK %W 3# - (#°#IT 3#T# itf# - 
U) # T#7STRT flWT #5T %ft. 3RH, IT TTIlfl 17 ##ir 
IHIHTIT M^dloil 135. , 


(i) RIRIFT Vs - 7 = 7 IFRTF eTFRIT. (ii) RIRIR Vs ## 
lt c bTdl. (iii) IRIK IHRT 3717.= 7 + Vs - 7 9 = ^ ; # vs U 
HRIFTWHT IRT 3TRTT. 3RIT I#R '^iqi 317 Vs(v?) vs-fRcSRT. 
3TTIT gilTgTTR #R 313# ITT?. , , . . - - . 

(7) Tt<sqi Vsv, VS + ^ - .9^. fi) XTRRIRf X-7 = 3 IRRTT 


(ii) gdRI R * It# ##IT (iii) IT7IR #W 3#=vs + X-77-°, 
Y IT g+TIMI^cWT to5T. /. 317 = o o o Y = ^ (°) x Y - 

(# #°IT 17 I + I = 7* 0) V7 = ^ HTHT (ii) I# 
Z#RT giRIFT I. (iii) IRIR #TKT 3# =1 + 1- ^ 7 = ? > ^ ^ 


/. 317 = 73333337 = 7 ( 3 \ ^ 

(^) 7i7°IT II, I + I = ^ (0 W (ii) 

dlch RT TJ^RIR % (iii) IRIK ^TKT 3#=I + < 7 - ^ = 1, I ^ 

• 317 = !(!). 

• • ^ 

IR 3 F# 7 R§^I^R fgg# 7 RsIT 

ABCD ?t 3#t gu TRsIT ^IT #, AB 37#T CD t 
sn^I.fwruilt^tl AB + CD HIT, ABCD = Ik 3^77. 

mTTT J^'J# Ik rTT M ^ u j K - HT ABCD + M, AB CD + 2M, ■•• 
ABCD + !M 37# ITTII RTTI s*#q»< u l ^HTI7 

f|ig# TRs^tT RTT 3171# IT# IT^ = A \ C — ^ ^ 

TIRIT 3ITI HHT# K #Tt. 

3 HfH : 7 RRT, AB = 7 1 371 # CD = ^^s. /# ABCD = 

3 #T AB +CD = 71 + ^VS = = I x Va = M. 

37 TIT, ABCD = 71 ^, ABCD + M = 7 ^^^ + ^^= 

ABCD + 3 x 7 ^= 71 1 ^. ABCD + ?xA= !!!^ 

ABCD + 77 x 'll = 3 °°vs 

ABCD + Vx ^ 0 H ^ > ABCD + I x TfH = ^oIVs 
ABCD + V 9 x 7 f<A = ^ 77 ^^ 

ABCD + I x 'll = ^ 7 IVS 37 T# ABCD + Ix'Iv A =^^^^. 


HI It! 


^ #TeT 171 3 tK #T, 


‘ J|ff left ' 



51 C * V 9 

x% $ * 

^ o o V 9 
3 o % 

* X* * 

^ X 6 ^9 

3 } 

= 3 0 3 (K) U 


W, ^jhk : srat ^ = - ^~ = 1 O 3 3Tff&T RT R?R 

d'Jtql ^ = ?o^,m=^x'a I ? 1J I#f«t K= H. fft^T K ^TRRRR 
37R> V3 %c8T 3Ilell. 

3T?lNr ABCD= fft % R fRRRR TWIT ^del) <R ABCD = 

+?$=$$ = ^xVs, K=V3, 3#T. ft BCD =iMl = ^ox 
= siql qi^ /. vi^ql RR^ = Xo^ 

.*. ^I C I<M ftgilt WIT 
= ?oX V 3 V 3 \ 3 V 3 ^V 953 Xo^ = 


filial Wqiq*H lRe*T R 4 U<ui 

'3WI3W3RH3?', eft 37SR 7/RRT RMerdlcR eft fg^ STR erNM 

3Wc ^ 1 ^TTeT %eT. cFRR eft 3RT<i^eH3 RTReft efft RgerTcf RIeft. 

^ T> 37 3TI f &T ^ ^ 'b) u leqi$1 f%Reft R ?T RRT RFft ^pi RRJR RT 

^d R 3> WIT 3T?ft RR% Rt feRRT %R RRNIRH 3TRe^IMI 

RW«Mlcb<ur fo rd id. 

Wm ‘ *= 6 ?*!= 

6 ^ oc ^ 6o ^ 




R^wi-kT 


6^oC$ 3TTftfT %6o $6 37% RR 

STleTT, 6 + ^o +6$ =%'a'* = $ +6o + ^6 (i) 

3#T 4’ + ^o' + ^ , = ^+3^ c ’ + «?^=5^^ 

^ + 3 °’ + ^ = 3 ^ + %V°° + ^^=U^° 

3T?ft eftd RR BOMiql %%R STTfift eqi-^l q j lfql %%R (Ho6e). 



fetjffi TWIT PleMURRft 3)l<J|<sfl RR> fteT 

TTTRrr, A = ^59^3, 3 hH Sl'qiiqi 3 el T. ell ?FT 3TRf<ftcft RRj *5*3^ 
%eRft (^TTcT d>ldlift 3TR R£R SRTeTT RIRT R%). ReR # <pi% WIT 
37%t wr Rft (eMIderll 3R%R 3735 A efteT 3H<=bl^H ST^pfift efiRR 37%eT. 
7TRF5IT, B = V9t-\33. ^AIB WIT% %%%% ^ ^T5T- ^ 

C = 37lpR D = 3*^ MC^D R>RTR f?T^R eRMI 

RC, RD W*l 

RC = V*3°, RD = ReR 

A ^V9tA^ \9W RD 


B V9^ RC 

37% %3R eRHt W 


llut*V° = WIT3TRft! 

. 

A =6^^ 3T#T B = RlfteTT ?W ^ieft Ri?R 

37TWIMT, IUtU^^ (X\* ^ WIT RTTSeTT ftf^T. 

fsgrsft icm %«isft% ftfrrpfw 

7RT 37%ftlRft RT^IT fR 6%V % 6^96 WT qil<.q>l£Ml 
chloild, %R J ll**left H5iql<iqi4 ft eRRRT R7RRRT RRi HM=tvO %%. 
eRRRT, <J lft>ld 7TR7RR’ ftRTef RTRTpTR WT R5?TT?t fenf^erdl dlderdl 
TRt TJRTd 3777RFRT BtedMi ^ffteT 37lft. RTHUT JJ«H6Kld 

WRT ^erl l ^ IT 3RTTRT WU\ TO feR Jcf 77WTR J j4xrle% 


STReTTeT, W M4d1d WRT 37RTRRT RRR3RTTRT, %RFRT 3RFTdt 
q.mUd^i nf^Trft rttIrt >kv.<*r 



RRRT RRT RTs#T RRRT 3R# 3TRTT RTs^R ‘<JR?R WTT’ 3RT JRRRT 
#fcT. RTR RTI# ^•Wchld RT Rld'Ml RTsRTRT f^Tc^T, ‘WOT’ f#RT 
‘#3?R’ WTT 3RR# %#RT 3T|daJdl. (R?T : ‘RRR % R?TR RfRRR’, 
WR: HeidklR® RTR 6?>, #TIRT : '^llchK ^). ^ RgMUidlR 

RT RRT dmc-RI 3RT#R RT RTR cRT, cRTW d,|o6|;# TRjcF#Ri 
Wtc^TT 3RT RTRTR eTRtoT. RTRR 3RR, fcviH) RTRR f#RT #TRR 
%cRT=R RRTR W #R, t # 3TTRRRRR 3TfR#T 3TF%, rM #R 
#3?R f#RT #3TRTR #R RT#, 3RT HI#HHM RRTTR RRTR. 

RRJR 3TRRTRRRT ##RRTRRTR 3RTR TJRR 3TRT #RFRT RT WRRT, 
‘fg^f Wf #R RTR RRRf RTRR. 

R?l#TMI#d1 f#M #3?R WTT# RRIWT 3T?ft 3TT%rT. 

T^Xx^Tx^ =UUU!U (RWR ^f^ST RTR) 

X 33 = ^0000 ^0000 ^ 

*X3R^*X3 x X3 = %ooo%ooo% (TRRRfeRtf) 
^X^4RX3^X3 x X9 = ^oooooooo^ (TTR 

ijH^oisxis? = UUUH Ofer rrt) 
U 0 U»Ux <t,\ = %oo?oo^oo% 

m x?o<!= TRm 

xm.^x^s; x xxs; = U3 X<^rx3 3s: 

RT $^3*RW3n *)dd^l f&g$\ W#R RSIdki#, #R#R 
RSRilPd R#R #RTfR’, 3RT 3RRR 3#R R RRRRT R#R 

%#R 3TT%. RT R< U IMI 3Rf : x# WRT * RRJR ^ R#T RiRRR RTRR 
Rlc) R RRT RRTIRT RvRFT RRR Rlc) #. 


QL ®D 
© r . £) 

® r , J& 

® r . ^® 
dHD 

© 


^?R TR^R # WTT 3?Rft RRRRT ^T. 


xx 


■ J lRi!dM'<l <ST#<M 


• chlM^RR WRT 

RTJ# WTT# R*f #eRTRT fRoSRrlRRT WTTR RJTR tfWR 3 ^^!^ 
^Xo^RRTRR, RtIR^RRRRT ERTRTR RTef. RR 3 TRTT WTTRT RB^IRT 
RiRR cRRTt^JR 3 RT# cRT# RT#R RRR %Rt. cRf^t ^#cT Rilft : 

^x(X + RT 3 $h]t*II ^RfR. 3TFRT 

^ o + ^ul'j) RRT RR^RT Rxf ^RRfT #R 3TT^RRT R^ 

R3#ERT ^O 3Rftrj RT r!r RRIRt t#R RiRR 

3TRfRR, cRI^oS XR’RT (3T + R)’ RT 4fRRi ^TJRR ^RfRTRRTR 
RRRToST %RT ^Rt. 

VV = (^ o + = T 0, + 3 xT o x 3 l ^^■^ , 

tR.: + 

= yoo + ^ooo + 

= 

.^. (3T + R)’ = 3T’ + 3 3TR + R^ 

?) ^ = (?o + ^•a)’ = ?o^H, ddciilHT 1 ^ =blxodl ^Rt. 

3RXTI# RcfcT RT## #R ^RfR# 

Va + = %°° 

l^U|>j) ; X<A # <aH : # l°o X£[RT 3Rf# RRiRRBift. 

TfTR \ o o^RT ^JTRi 3RRRFRT RRcoRT RTsRT^RT #R#RTRR # 
RtfRTRR fMt %T RT#. RfT:^V3+?^=^°°R 1 R, 

3## XX + * ^^3 

^) #R 3T#t WTTR RTTR^RRT# fR## RRT 3RTWRR 
^V3 * = 66 Ro^ 3Tlf# = 

fR # #R 3RRT# 3RRRRT tRRT ^ooo xjTRT V3o^ ^#. 

3RftTT (V 30 ^ ) ;i = X^X Ro% cRId^H X^X + ^o % = \so^ fto5^. 

X) RTT#RRf# R Relcfl, RR 3TGTRT RRRTRT fRc5T#RRT RR 3R^# 
RT^RT R 7 ! 

(RRR^y = X^X l^R<{ 3## oX^X = 

^TpHcft H‘Kld[ XH 



RR 3fl3T3t RHJJR fcTRT - ^ 0,000 VsV9^V9 RT 5 R RSRToST 
Qc1eRI<H (I9l9l9l9) ? = 3#T $0^6 + = Rl9l9l9 

3T?ft ^ftcT 3T? £]U||0 f^T# 3TTeft. 

^teT 3TlfuT Rl9l9l9 Rf^TT RRfcT Rf^ff f3'RI°fl RtRZt 

?^3*? ft ilHId^M ■Htei|| 3||eRM w R J WisRI 3TfRRTR J IHdl<K 
Rl'ddld. 

*0 WRT? 5ldlod>dl 5ldloddl, 3 3 3 3 3 ?t 3T?TlR RTR 3TTRrgf WIT 
R fddl \oo r oo 0^[ TJRJ V9V9V9V94 ^Rft eTFT^. cRRf Rif : 

(3 33 3 3)’ = 3#T ^19^Y + 

(V9V9V9V9£)* = 3#T ![^a+ ^ = \9^\96 

3RIT 3ll u l<a)d iff ROMI diKodl %ftcT. RTR (RIRIdl RftRR RvR% 
dlRdld. 

R^f M*HI u I t 'J'Wf 3RT^RIT RRT •HOHI RlM^R-UHl R|<icR| 
^JHI* ^R^RiT ^SJT 3RT RTR, ^t*TI Zffl IJ^JR VRTIRR R^cf^T 
cRT^3% TPRTRR R^. RffRdlRH RTRf fRR. 

• <dl^«i Vigil I 

?^° R|<nl ^ I CO-HI •Jiml^l RT WIT RTM)r<MI RRRRRT. 

Rif R3*R 3fl^RT WsRIRl IRRT RRt RT«jt ^H^uf 3TIR^. 
r^IRSH WT 3TTsRT 3?fo2RReRT RIRfR. ^ ; 

(?) & = ¥R X R | 3TR 3^RT 3 R Rif 
3TR?R. 

UTR RTRNRT 3l|U|<gl Rffiff RifRWR iRTtSPR %cRTRT RT VTgRT 
Wff RTTRcff VRR RR# 


(?) 

KV= 



( 3 ) 


3 RV= u’, 

\-V 

(*) 

^vs 

AJJ 

O 

II 

so 

jcn 

so 

o 

o 

^ 

^00 = ^ o^ 

(s) 

\%°* = 3 ^°°, 

3 ^ = V, 

so 

o 

o 

II 

SO 

O 

(O 


%o^v=^V, 

**Y = 


^ irf^W '<1 wU< 


sffgRRTR, Rif R^R 3TT^eRT Ris^Rl Rfe R^R fHcdUrMl H^R 
RRTR Rif 3TRRT RTR^R fa'Ri'f 3TRT fRRRt Rt RRR RfRv^R R^R 
r|r Rif 3TTRc5dIR. RR, ^mIrR iJo5W}RT 3#T RRRtR^RT 3TRR 
RR1R RtR. ffR?T RRiJ^RT iJdfcTT #R cfc STRcRTJS #T Rif ^TFRT 
RT WTTRT RilMWidf RRT^R VisRT 3TR RRfR RTR f^eT 3#. 

%yftR RRRfjoS ^RT 3TTRfRRi RT^ 3RRcRT RTROR % 3 r|r, 
rRfRT RtR fRRT 3lfRRj RRHTM3I STTR 11 ! RRRtR R^ RTRTRt. RRT^TRTFf; 
RF^RT dR I sfijoi , fRRRT RRURTRIRt RIR R RRt #FRM3t WI 
i^ujR RFRcTT RFTRT RfRT RRT fRRT Rc^R #-'5^RRRT RcoRTcT 
3#TRT# RriRTI RlfiRT fW ^^RfR R?! °RRlRft 

4)d u R I RR dT 3TRRT RT^ WT dld^ldl fRTtR RBRIReTT, 3 ||R>^r1s1«Icj 1 
j|U | chRR IRIJJR RR RTR R^T ^JJR ^TRlfRR RTRTRcR^t 3# RT R3T% 
HfRR RRR R|fRR RRRtR 3R^R. RRR RRl^R RW^RT 3TRWR RtR 
fRRT 3TfRR Rif RRTfRR 3TR^ 3TTRcRTcTT ■HIHSald 

3 <l^<u||sf ; s.ov^ = *°<^ %S%, = ??’, % = ^ 

^ ^ = c\ ov = ^ 

= V, 3^ = V, £\ = V 

VO ^o'*’ = ^^ 3 ^ X$ = '*\ 3 ^ = %\ X^ = ^\ ^ = *’ 

VTW, R1?t Rf3RT RTsRTR 3, V, ^ d J R<alel RHlfdH 3TORTR. 
dfltfg T ^ : ^ TT RTRTR. 

R>T?f 3RTRIRRRR RRT^R RTsRMRR RRRtR^cRT RtR RRTReRT Rif 
RTsRTRT ipilRiR R cRldl ^(l-d RiTFT STT^cRT ■d’o^Nl 3R°RT 
RF^RT Ris^l'cRI ?dRl WT : 

(0 ^ = - 1 ^ 3TTf&T(Xx ^) + (x+ <0= 3^ + U =*% 

( 3 ) 3nf&T ( x^) + (^ + ^) = W* + 

(?) vs’= )M 3 #l(T^X %) + (.^+%)=^%W + ^ = ^^% 

Rtg ?T SRRR fWT WtR RT?t. RRR 
y\*= RR (?x ^SM? + + 

= + WVa 

R^T RTteT fRRPTTRt RrRRT RRffRR 3#. 

W^RntER RfRcft RiRtRT 



• ^wdiycj #n (ftinK ^fpt jstf) 

*k#dl T3^=F 3^5 3TIo4hlci|H BfdMI dfeH ^TPfR 3T^TT 
3?^T !Jo5 Z^[ ETOTR tcT^T ^TT WoR 3Tdfcr HoiNI4p ^ 
WIT «Rrf fcfeTT ?IIMOT WIT **u|dld. 

flcft : (i) WT Sldld^ld df?RfT 3RTRT ^cTTd «Tfc 

3<elcdl 3I#r TJo5 dTR! (ii) % Tlf|RIT 3HUslldl 
fdt?l. (iii) RT^KI 3fd> 3HH sll'bl *)<s^d 3jcb]<t 
^Jo5 cfTT^T, cl dftRTT 31^1 ^oil^ldlO 3^2IT fftHdl 
fcl??l. (iv) did <-bdl 3RTRTRt' dRR 3nielcrll 

3jdld ^55 3^0^! 3kildl fdR?d ^tcT dft ^JoS 
wMl Wft ddl WIT fto^. #^I i^ddldd ^oqy. 

SeJlfTR * : 


wt 

* 

Y 

V9^, 



V3 + 

6 = 

Vlt 

3 

Xp3 

>. 



X + 

£ = 

wl 

3 : 

: 

<■ , 


*+V 9 =U, ? + ? = 3 , d^T, *V 9 £ 

c^T, XV9£ ^Jc 5 ^s^dT SRPR; 3H | oil m oil d dfe ^qp 3Tdfcr TJ55 
diltoH 3liHedieli 5 3 3 'dt ddt ■HOMI facile! did ^^lellNd dodl ^T. 

ft^ledl WMl 3id)kdldl pfRdR 3T#d ^55 fcd^T 3TRtedT 
3 <^iRc 1 d^-dl ci^ct, ddl<dd> cjii^i^ci chmldiiidl edTd faid<3ld J l 
ddtf fdRT ‘^RTTdt dfe d5c£T ifalMI WTl’ 3TCT HWddui %el. 
^^<“1 3 : 5*3H t ^ 3TT^st WIT ^ 

dldfr 5 > : j >, jx3H, X + ? + H = 5 > 3 , 5> + 3 + 3; 

/. 

3 


3H, 5 + } + ^ = !>Y, S’ + V= H 












• RdtmfWJT : «TfeT fTrfi q?RTTTiT Wdl 

^tfftSTT 'jfT^T sRfi SRT^eft WTT ftrF ^ WI ^R^TT Welt *lRt. 

3<l^«ll«f, R^, f zf R ? ^ <^TWT V9 Rft. 

?RXVa, f 2f ? ^ WTT ^TR <aX RR. 

w wt, RtrR wt wtt fawner wim c*tt R#r ^Rt 
3P=Ft wMl trRt 3TWTT. WJT TWT sRTeT RddMR WT WIT 


ifuidld. 


3qf<«ll4, ^ ft 3TRf WIT Rw Ro o 0*3 ft RtFR WT 
WTT ^cTcft TTC 

Rooo \9 = \3X^ x ^V9 


Tfu^T, ^ o o o 
T*Z 3#. 


V9 ft direr R^tiMci wr wit ^ rwr # ^wt V9X* 


3WR wi ipii w!41 re Rw fredT rep drerrerr dfei 
RtPR WT WTT% dTTft RjR f^t 3TT%cT. 

U) vaooo^ = x V9<^ 

(R) XR& %\ re Rw ft <IHId,dH WTT RR, t 

3TNedldl 3I3^F 3TT%. dfT : 

= <>* x \% 

(3) 5W=*o^ x ^, ^o^=(oo ?x ^ 

(X) RX5|X? = 5>o55. x R? 

(H) 3°xxva^ = \ 3 o^% x R% 

(O = \%MR \ X ?? 

3WT <ldld sjtelT W)K ^<1 HcTi-i 3iid>SHls d)<M 3TPTedTeTT l^^aiyi 
wNdT Mdtd^d dfel Rif d? W1 WTT reddT RdtcT. 

m Rif WPT odd^<cb red^FlRlt J3ft Rp 

%T^eT dTft. 


WM 




^t. dT. %. dTf WTT “dTddt irf^TcT Mold'd” JW M<^l 
V3V3 x 3? = ^V9V3^ dW U $ r<d>H< WT 

WTT PT<^THI- gT RR. d W ^V9V3^ Wd Rif dd W fl*H ^ffT 
RfSZTT 3TW WWT RSTdRt \ 3$ dldidld! 

• OT^teld? wit (stfRt^RRi Rdtf) 

^rt sidR w^tt wRt srerRedT 3 twtt drirerift sraRr 
TjTJTdr ftd^r fP (fmcw Rt wit RR Tit wRe^tt^ w^tt 

3TdM ft35fT H#T 3?qTfaT W^ WWdt t^RPT RiT dUMWidl 
?rt^T dn^rt. w ^tt RdtR RtrW itt^tt wtt wt disaid ctt ^t 

^TZcTTcT. ^ U RT 3RTT dcdlRd yodidl 3HI^I<dd) WdT 3RT ^T^TTsf W 
Reid -3TT%. 


TT^i ^STWTT STdiTdT 3HIMedl w 

^RTT Ret. 

-i< | f<U T : t^vs WTT ^ X fT 3TdTRT ^35. 


? ? 
i R 


l <A 

i o 


3TWT 


■Q^STR V9, '5 tI Td) V 
.-. lSx^ = ii 


Hx'<=T 0 


% x V = V 


o ^ 

R x 


i x 
* * 


* t 
R R 


\ x x = 


X X x = \\ 




55T, RV9, ??, o^, ^X, \L, ??... d^drRt- 

dnR Tdl u IMI WdT Rrasclld. TW 3TKtef^ RTsdl- 

r Trffrrat d^rttdT •Tii.'ixi+i 



PTPTt 

UT WIT <Tll^ PTsPI WP pvp 3 pf?ip> P 4 oA|M| fq 
P>i c l<M 3i)ai<ani %M. PT°jHt PTPFF 3TT^PT 


ter fo?cp 


*PTPTP 


U) = 

= ?S°*UH 

(R) '**=$'*-, 

?^= ^VSI=£; 

*V = u^*S; 

U* = SVSo^<$ ; 

(?) 3H*=?S°^H; 

4?* = Wtfni^u 


PIPPM #?t. pit - 
VS^ = V3V9^ 

h ^ = 

R^ = U6t>t 
^ = Y?^V»$ 

U Y = ^>U 


00 W = \ a% ^w, ?r , = ??VOr***, 

U'' = SH° <? S O o*<* % P^t WIT 

(H) U* = U^S^UP 1^ WIT 
U* = W$UU 
(«0 H‘=U°TUH 

•Hicbslu, ftldidi qlcil^n SR^T P^ft gi^MI PT W ^ld-M TPT 
L hi^ c H -3SPI PHfH fcTPcPI fpp qldloSri, cPIJ)Hl u i Pilft -HIsPI^ Midi* 
QckrPIPI fnallcidMl PP?tp <b)u|cMldil ^PlPt TJo5 PTsPT TC 
P)s<*pm Hiq>sMm<si] f5#]T 3d<m')cld) PfeTBp arpcPigs 
^Tcft ^'lco-41 'JP^hMi PT WIT 31T5a4d4|cK P>N}p>lj4l pipi) RRap 
(PPit PPTf) 3W cPTP HIHP>< U I %d. 

• Ipfp ■HWi 

•taPfa WTTSPT MdldlfH PI PIPP afr aid di< l PTPTP. fp£tePT 

wt^i ?pppt pt#pt f p pIp *ptpt pnppt. a^ft wjt 

f?TPt elMIdl PIT 3TTWPT PPTPt fiMt 3TRP *R?p PTPpJfTPTC# 
r^IT ftPdld P u fd TF^TrT PHupiUlcj) PThAph 3T31T PTsi)dl ‘^ifp 

w it’ f^PT ^ih«h<* ^it’ t^t[ ermr^T. pit : 


3>IhW 


*1 -M 


(O V£ = *x %R, 

(R) vs^ = 6 x %, 

(?) = %o x 

(Y) = U X 

(H) ?U = 'Ux^, 

(O HU = ^3 x Vs, 

(Vs) = 6 R x u, 

(£) UH = U x U, 
(<0 UU = U* x 

(^o) w X ^VS, 


^ + 6 = U 
vs + ^ ^ 

^ + o = ^ 

\ + VS + ^ = % 

? + ^ 3 ^ 

H + * + \ = V3 
^ + O + ^ = U 
^ + * + H = 

^ + ^+ ^ + <^ = 

^ + ^ + ^+ v=^vs. 


<H I H* R WIT ^vs^<^ ^l^<gld ^ WIT apt. PIP : 

^vs^ = U x U, ^ + vs+3 + ^=U 

TO, cbm^ f^nra ^^vs^ wit ant. 

^^VSV = ?■*? x \6, $ + % +\3 + V = %6 

W vfpfiwp aiNePi eiw apcr^r srter Pit, stpt MvrPi 
^Is^ TT Mp W\ pfldt. 

• «wl 

PP?t ^WTT^ PP Pv^T (MailclcPI ■HOHi’oPl 'W'^MN'^'I PT 

artsiIPT ^PTP. rMI'Hldi PP PI^P 3Tr^cPT TTT^ZIT 3TPIRt 
PP %^ePT wtortpr: PTTcft Plf?^. WT 'Jlldjofll^PI WTT fPSP^P 
TP ^tP. v^ u |P TfP ^eHdlPTPt 3TP PPP 3ITP3P ci^l 

T fppp {Pa!>PrP rpt PTPPT ?t^. ?t W #1^ c b< U|KI 

PTP^P PPP^PP 3RTT WTTPT r fpPP WIT’ Wl vdl'Kri. ^ : 


(5>) 6* = W, 

(R) = 

(?) ^ = 

(V) 

(H) ^V=^W, 


H + ^ + R = C 
V\ + <^+? + ^= 
X+^+^ + ?=^vs 

^ ^ ^ + ? = pis 

^ + VS+Va + VS+^=^^ 


pfui# HMitPI 



fig# t#f to#rt 3 # flfw #3 ## ##3 g## 3 rrt 

g'WSTT 3iq»k<^M 3T3TO5 3|3 f33^<H #T. | 3T3TO5 }#3 t#f 
WTRf (#f3TO t#t 33#) TOT 3R. 3TRT ^ #7s3T3f 

^#3 3 im<MM) 3 g 3 %# 3 #. TO RRtTOT #WTOT T 3 HM fTO#R 
3RR <*ihWh 1 fa^cRl-H sjhs^i gs# 33# %# 3TI%. 

^iwi : 311# TOs3T *7 TOT TO# 377J3 # TO 7#TTOT #3 
3T# TO#TOT ## 3T3TT# t#T < 7^3 RT73 TO# 
TO# TOT #3 3T3#3vf nidi 3# cn^M 3T3TTOT 
tf J i#i g3TOT 3733#TT cTfR 37TRT TO TOT #7#7T 
Rx©c;4]<H #7s 3T ^Rctld. 

TORTT, 3T# #TOT # 3^RR ^1§M\ TO, 

3 = S x 3R, ## 3T + 3 ^ ^ 3TTf&T 3 ^ 3T + % 

f#» 373 ft TO 7## #R 3#t 7T7s3T 3# 3RR TO 3T t 
TOT### 3# TOR 3TTfTO 3 | 337 TOR 377%. 

5TH dMfrod f# # fl #, 3T 3TT# 3 #tR 3T iTO'Hdl %3T 
3T3RR? 37# 37#gTTR g#R WRT 3?T%. 

3T 3 

0 *,&,%. 

I 3,3,*,^„V9,£ 

9 3 ,*,i^,vs, 

* *v . 

3 >R^ 3 v 7 Rf enrlc^i ^ ^ 33 ^ 33 # 7 T 793 T 

# %6, *V9 , 33, XH, HX, 33, ^, 

\0C, *33, UK, \W, ^o V9 

3*3, 33K, W, ?o^, ^X, Xot^ 

#TO f|g# tr# ###T ##33# #7#3 g#R TO# 7#T 
gRPTOR 3R3R i)u|MI 3#MI #r TOT#7f 33T TOR #R# 3# t 

^ 7 lP | ldlH<l 3##R 


giTTOT TOR #RTTOT 3## <# gTO 3RRR. 3f333R, 333 TORRT 

3# #’ tort to grorr tor 3# <7 - 35 stcrtt #1# 33# 

TO, 37 = 37 + 3 33# TO# TOR 3R3T7 #RKT 3# (3- *) tc5T 
33RT 3lf|^, #3, 3 = fig# TO#TOTT RTTOtTMTO 3fTOTT-TOR3T 
TORP3T 3# - 33# 3R = #^#3 WTT * %. 

333T fig# t#f TO#7T ##33# 3R3T 3R#TOT gR3R 
gnp, gRT3TO TO#3 #TF3T f3#Mt3 TO#TOT 3T3TRRT 3RTO5 
3ITOR i#pjT 3#Rf 333 TOR 3Rf, TOT# TOTTOR R^ - 

(0 ^337 t fig# trot TOTOT 3 gR3> ^od f3^33f3 TOTOT 
TO, ^=3T3=^ /.3T= #TOR33#3= 3 > 3?+ \ 

3T + 3= ^ + ^ = ?=3T, 33 , 7-3T= < 7-? = ^ 33# 

3=3 > * i 3-? = 3- 7 = ^(3- trofcTRT 33RT 3#) 

3T3R3, ^ 3 ^ 7 x * °d = % 3 3 o ^ $ 6 

3R#3#R TO53T 3# f3^3#3 gR3i#. TOTTOT TOTOT3% 3RTTO 
3K3K #TO3T 3## 3# 33^3. 

(3) ^3*3 37 fig# trot tosr, fNM# gRR 

TO, /. 3T= 3=x ^ 3T+ ^ 

3T + 3 = ^+X=^=3T 33# ^-3^=^-^^ = ^ 

333, 3 = X /, 3- \ = X - * = 3- 
3T3TO, ^3*33? x = ^Va^XXX^ 

(3 ) ^ 3'3 ,< a'^ 3 3 ^ fig# -SHril TOTOT 3 3 3^ f3^3#3 gR3i 
TO, = 3 ^ = 3T3 /. 3T= 3, 3= * > 3T+ ^ 

3 T + 3 = 3 + ^ = < 7 = 3 ) / > < 7 - 3 T =^- , 7 = o 

33# 3= H .*. 3- 7 = * 

3R3R, 773^^^377 x 37^= 37'7 < 77^ 0 0 0 0 ^ 
cb#=h3Rr 3f&mt H'Kldl 3)<TOdil 



‘RT'W fRWflRfcH %njRT 3TRT ^Tf^eTT R cRTRT % TJTRi RR^RT 
RFJRT M 3TRRo5 Tt aiRfFT RTRdld. RTR RRft 3W^J 

3g$<«i||<|H ft f^Tcft «WddHI fMt. RfT : 

*333* x S = \%o66<t 
Wm x \6 = ^*Vs V9d 

RT 3"<l^<u||d ar^RRT RT = ? 3frf&T RT = 3 ^.RldlTT, cR % TJTRI 

6 r vs rrt: Mr. TfMt ^trt ^ r \c *rct [r^Mr, crtt Rfter 

RlWld RRR RlM 

(i) x %°6 = *3°*W 

%°6 RTRIftR 

(ii) *3^3*x = *^3^ 

R®t RT 3 3TT% RF 4<R> 5 arfMRR dl$ll f^ldM J ju|d> Rift 
3FIT 3mRKIc*IR> fMIdc-d rMrKM) RTR ^fw flcft cRT% 3c#H 
TTTRRR RlM RT, f¥?T£ Mft WIT RMdR 3RIT 3TFflfR «RT Wf, 
clfsl Road Ris). 

• fcRiRl wrr (RRT ^RR Mf) 

RfT 3TRft WIT Mr fRRRT ficftR WT Rldl-cRI Mr 

fariddl Mr. cRHIIdl WT RfT 3TRft RTsM RtR RR RR% dl'ldld. 
£IR]r*j 3 RR 3TTRt Mr ^)uiMI wtRI Rffcff RR RT 3«fcft<*^^ll 
M 3TRft wHl j^RT, 3T% M R7 RRFT cRT RcMlR R|u|dl$ 
3TR (Hc6RMRI. RRT dl'«fl*bdR| 3 RR)r^ R 3RR1R4R I 

M 3TRft sirIrs %^R rM TTfT 3TRft MI facacl. fcTft ^RtcT 
RRFTR RR ^ 4 lci R<M 4^1 RT ^dld 3 h|u|<s 1 RRt TTMT RTRTRRt. 
cftR RfRTRT ^1 4,^1 R<fH 3TRTR R°Rf R^IT RMT fRcSRRT MlR. RT 
44d1d RlMcrRT WITRt RcftjR 3RRRR cRTRT fcTT<RT 

^RT WIT 3RT RTR Mr RlMM cRTRT 3TTReRT WIT RftRTTTR 
TTRF|R Met. 

3RT?TW?f, ft RfT 3RR^t WIT 

fRft : <a ^ ^ V ^ RR 3T^t RR 

RtR aM 

RfRRHRt dilMHT 


RT Rr^Ri RRTR RRRT, R fRo5R^ RT, 3 

3Tlf&T ^ = W 

3TRTT rRRRT RTRTRt 3KdM<d RR^T 

#r 

cRT R#cT, RR 3TRTt RZ, RlR 3TRT 33 

RRR cTIR ^ 3TR) fHo6<JH, + ^ = 3Tlf&T 

33 + 3 

3TTcTT WIT ^<e|H 

/. R#T WIT = 3 

^fi Rtter Mr, rr ar^t -nz, 3 «or* + 9 = 3H^^, RtR 3rat 

+ ^ = ^O. dVl< RTRTRt 3TRRTRRR RRR 
# TTM =^ 3 W . 

€tq : ^ ^RRt %, 3 fcRIRt RtfRRRR, #RT RFTl^ 
3TRi ^R fB'. 

3TRit 3TFRRtRft RRIfFT Mr RilReRT MlR 3TTRcRMT fcRTRT 
^ERT RRsRT RilSRT Rf&Tcft RRR^R) RJ^R M ^fcR. 

W RRsRTRT fcTRRT #MlT WTT MfRT ^RcRT RFRRIR R>N^T 
ifuidld, cRTRT 3eRTfT ftR Rift. RRF RZTRt 3TRRIRReT ^R RJRR aft 
RR, % RToScT RTft. RTR ft RfMT R^RM RT^RT RRft RTR^RT RRTRcft 
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• TSltfRRRT TTRTfSR TFRTTRT M 

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RRI RtfRT RRR fRRW ft^T ftet, cRRTRRt ftRTRRTRRT RR#RTRT 

HV 9 


R^ftRRRRI RfRRt RRTtRT 3>T4>i<bl 




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3Tq> %ftjf f^TO ^Is^ld, W^R sNfcf ^^T^qT 

(?) WTO 3 PFHt ^ 3 T ^ 3 # 3 m WTR 3 T#q W?Mt qpt 
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£*'*, ??^, SV\£, W?%, ?\ 3 \^, ?\?$, 

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totot ~&m tow 3ft. 


h<: 


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x * = \ °6\, * + <^ = *°, * - * = o, %- % = 6 

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*°<^ x 3 = 33^, ^ + V9 = ^ o , 3-* = 3 , \3 - % = $ 

\°6^ \ V9 = V3^3, V9+ } = *o, \3. l = } . Y=^ 

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lo69 iX % = ^6o\, ^ + ? = ^o, l- \ = o 

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W^ft W?RF 3jd)M! ^i^dj (\o . W«H*k) fa) ^ ^ W WHId 
lk ^ **)Hldc^l 3kk|| d J iidl J l 3TT«jt% 3k %M. 

cfkrr^TT ^tr?t 3kt *k?rr fer wik w =frt fk'rw #cf, c^rrar 
riw wi RHlfad, Bkr, 3RTT ^o<s<^ ^kdt MI£)edHd< 5>i qk<H) 
?tTT *)K<rlc 1 l 3n|. r^midl 3rf«RF 3kfalT TOM WdT W 
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C Ct ?V9^ 

C'iX 

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U) ^ (<0 ^6 (\°) x\6 (s>5>) (U) U?) mvs 

(W) 63$ (%\) (^) \9^H (?R) V9?<^ (l£) ?V9^! 

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WRI dlddld. ddl^iunsf, 

U,6R TJS WIT ^cTeft Wi (%) (3) (?) 

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WTRt 3T<dN<d RRRt dTR^. 3c(R?RRT«f, 

^TRT RR RdRT ^6 RTR RRdT ?R RT^ 

%dt TR ^ldl J k + \ = 3Rfd3dRTR7 $6 + \ = 

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pTbildl. RT ^kTM RRT WTT PloicldT ^xM. 

3TTRT RT ^dtR RRT RfRRt ^JRRT d^TR RTRdt RT^R 

WTT RR W^R fidRRTRT RT?R 3TT^dT 3TRT TPR5 RRTTRT 



'jpft oq'Hl-cll RRJ 5ldqi RTR ^effSJR RRRTRT. RFR^ Rf ^flM^l u i 
3Rs^cT [HoAcii^-cii TTj^t. 

^ : V9 + ^ = *, W R*d; A + % = vs, R*t 

^ + * = o, l o RR^! 

?t 3RT eFST^fFT MIoAcTI R)f qiM RRR d Rs?T : 

(3T)RTRtadMT \, 3... ^k. RTR ^ ^ToSfr dcTdt cR RRRR %deRT 
RT 3Tlpb^HrK ?<v3JT RTRffa ^Jo5 RMT 3TRrM #! 

3?ng<un«f : 53 * 1 ^* Tjps wrr sttPr r^ ^ 

fdt : ^3 *4 'a* JJc3 3Rs*TT 3#T RTR \ 

: ^3*4^* R1RFIA $3*K R3TRT RR RY, RTR l 
: (O ^4W$ (3)^3*^ (?) V9V95 3*£ (V) *W$? 
(4) ($) ^VV° TJFRt d^TTR *RT (V9) V*V9^4 

( 6 ) V 9^*3 (%) *?V 9 W (*o) i=AV?^o (XX) *?V 9 ^ 

(S3) $°V?^3 (.S?) ^9?^oVX (X*) 'A^S 

*4^ RTR^R ftR*R 1J55 3RsRT 3TTeRTR ?R RflFRT RRd. 

4 1 H rf ! 

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’JpS RMT 3H=ldluf fft. 

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^ItSJM *J3 MI dd. R?R. 

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(S) 3S^S (3) WSS^ (?) A?v<j$3$ 
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(S) ^ ^3*° ( 3 ) *4 V3«^^V3 (?) ^3 VHW 

W fcRFRT RFRdcT t%Z RMT 3TTdtl 3Trt RTf R!^ RRR! 
(3T) 3#T (SOW 3<l^<U|ld RoSRI %d?RT ¥RM WRT ddoi^d l. 


RldfylHIhsiJI dl-UsIMl RRR 

SP^RT RtR ftdMl 3TRRT RldRT 


3£fpRT f^RRlt fRRTRT 3TRRT HlddRMI dcSIRT Wm 3R?cIT fT #o5 
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‘^TR 3TT^f!' 3T^ ^TR ^cT 3RRT. 

^ft?r «Tk R5F#5qj srf^T^IT WRT 3T3IT : 


3?oV9^^^ + 




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3V93\9?VV9Y- 


^ 


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n?? p 


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^ oRT qiilddl ^Td «Rdldti fHoildl! 

tosr dw.RRlR wtrirt wtciT rpr ?«f q>dfn^dl 
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^R <l<siq<rqi RTftR. 


RTRRJTRt RT^ RT 


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rMIcUlci 


6^600 ^6 00 3 X£oo \ 3 X^oo I'tfCoo 

R X^ X3 X^lSX? X^Xl3 X^XL\ X^X<£ X^XX^ 

3 x^h^ x«£<^ x^v* x^3 x^xxk x^? 

x W53 W^X ?Xo^ 















































ftf<I * 


^*1 ** : 4i-h<1ci #Mf fFpSt^eft WH F fNzjt FIFTtF 

f^M^TT Fueloil FFTFFFTRFT FTFt 3TFTr)dl 3TFT 
Fldl F>F. 

trr *M 3 ^TT^drT fTToSI^^ f?RT^ wrdw tcflw^c^ 

WNfI FRFT FRJF F^T. 

WT^TT ‘HlH'Od fFTSfifteft Tioqi FtF FTFt 3lF>ooFMl 8 |)cFIf 4U 
f^R STT^FFT 4)Ci=t)iq<1d WTTFt trtF! FTIdM eft FTFT ch|<grlf ft^T. 

«biH<qnwT, **W 3 , *3W, Woo,^i^ ( 

wr ^terftre stpMft wn Mr 3 forw*Pi trtsr %cft 

3TT%. 

T : 3 + v+ o + V9 + *+ c a = 33 
3:<TV^ = ^ 

3 : ^93 

X : ^^oo 

<\ : *3 + 5 = 1% 

\ '■ FTter fmMI Mter ftft Ffta wiiM>1 

3TPniftT F<F WTT FF Mr 3TTWT MtF FRR FfteT tcftFt T§TFt 
FF^F #35. 

^6oo, V3V9H3, H3V43, 6\%\3% 

? : ° + K+ 3 + H+ 3 + , T = ^ 

3 : %%-^ = V85 
3 : ^3 

X : ^"€6 o o 

^ : 93 + 3 = ^ 

5 : 3^3, FtF fff MtF. 


^dd^FI FtF TFTFt 3£F 3TFFt< 
M*JF TFIdTld WIT fdfT EFT. 




ft#T 3TFFT 


wU< 


• arisfcrar wrrat *tiff 

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Mft. c^rnjjr MFtw Mf - ^ ffftf W 3n ^ t ^ 

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tm Ft M IMtt TjaTwfcr fft T\mri chis^idl FfFRt ftsft 
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3F3FRFT FTsMfT FfiFtTrtFi FTs^FT FTMTFFt (3T) FTTF 3R>RT, 

(W) 3R> JJu||cbMT fq>Hd)q'(., 3nqei^H 3RTeft. '^TT 3TRR 

WJT ^eT ST^RT FTFt ^ <i<llq«t> WTReR effa WTT ^ u dW 
•qicjd TfiftcT. 

^ . 3TR^T •HTsdl ^ ^ ^u|q> V 
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^V3, *%, U, ^ W 

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3. FiTFt 3FIFFFTF FttF^cTeft (Ft F^FT) FF FF STFeftRT FT TFT 
FFt% ^F FIF& FTF F^FF ^FFT 3FFf FMIIdM M FfFFFT 
3RFf FTFTFFFT FFF FFRITeft 3TW%t ^FFT %TTF M TFTFt 
MtF FFvF FFFT 'ft^FT. 


^FRFFT^, 3TRF WTT 'J’FFT ? FTFFF, R°, °R, 

o^, \6, ^^, W, °t> *°> °*> °^> °*» 

^V9 , ^3, oV, o\3, 3^, oh, ^H, TT, FTfF 
fqj^F 3 ^ 3T3TT Sti^lddi WIT tFoiSFTF. rqiaeft FfFFFt ^FT MlRt 
■WTT dl-dcF TF T FFFTsFT 3 L FF WIT faoicl. ft^T FfFeFT 
FTFRFT V* ^F=FT FTFRFT V* *t3R FFF FtF, % Fl^. 


||t*TT 4 ! H cH-^H eft 



3°, %\3, W, 06, lo, ol 

°Jj. °%, 33, U,' 0 *, U, °V 9, o( A, ^ 

K, 1%, W, K, 1%, W, W, ^ 

(yiefrll-^^) T^ 3<> TJ^J Srac^llH eft 

^fT srraeff ^TRTRZTT d^T %srnirf. 


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*x^+? 35 


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:. *%, tx^ + 's 

^ 6x^ + ^9 


3cq|<ft 


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faqrsq ^TTjft, fohdl 
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5 % » 3 

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%6 % X 3 

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3TWT cR RSTc 5 ! ^PJTT rm laleild RfKNdl Id-ddidl, 3W ft^ft. 




Wn^TT 



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fdid|HI * 3 3RRt W dIH'ddMI 3d#H dRdT %cTf. ^ 3TT%, "dtdd 
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m s#g. w anwqra# ^tt dpifddt R?Mi snfd, ddm ddtd#dT 
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W d fft 3TT%cT! 

*3 RfTRT *Mt, ‘rftdfZd>d 3T#f^R 3TP$ ffedT’dqT 
d#T, ‘tz fdfd dddfzf^ldR^W fafadlH dcd>R ^MT. 

cdT Rddhdl ^ 3 dUIsM 3fH%RR RR£T diNtdRIH) % 3% tjdtel 
RRJd TNlrqid H'lV'JM %eT. 

?3 = S+^+^U^)’ = ^o+V9( a + ^V= 

*3 = * + o + ^(Vo^)’= * ^ + V9} + £* = %%%= 

33 = <A + } + ^, (H^)’ = RV3 + ^ + \9^ = 5>^ = ^ 

33 = ^+ ^ + *, (^'tf)’ = X\3 + '*3 + \9$=3^=^ 

33 = 4 + ^ + 3,(<^3) , = <^ 3 ^, <=V9 + vs? + ^ ^ 

3 3 = <3 + 3 + 1, (W)’ = 6<a oocv, 6 <a + 6V = 3$<3 = 33’ 

dMTdt|d U? ^deff m, l\V = 3#T fddf dfddT 

3U ^dddFR, 3U’ = W33’ f d J R J ild TR^dfedT dfddT 

• d>ld}d><Hl iRrdl Rlsdl’odl 3HUIIsflH ddft dtZdl dddt 
*. 5 m <*>m)«M #U 

sm drift df WIT 3dfd d^ W ^FdT WJMI dZPdf 

%fNr ej)<«v»i ct>l<scll ^dld. ZdlFRTRf, 

J lfu|dlH<l <*NHj 


%, M + C \ = 

^o^= %% + + 66 + o\ = 

UV= \W%, *<\+ w = w 

^o’zX^t 00 , W + ^ 00 = ^ w 
diiMld>< Ht d R<rMl dT dldl^qT ^ WIT : 

\3^ = §o6Y, §0 + 6* = 

^o6 ? = UW, \\ + tt + '*=H 

o ? + V1 + 1$ = 6% 

dfedl dIR 9FTFT 3df&I %o5 dlcT^T 3TNcdldl^ 3RIT dltd %dT 
■^df. 

4>IM^<bR fi^Hicfi 3TT$)«f<r>K<b dddt 

(i) ^ ^o5I ^ S,^V3Y ^ddl dRdl ^dt. d?T : 

= ^ x (Ry) x (^ + ^ + ^ + y) 

= Ix^x 3*3 

(ii) WIT *?*IjT 3Rft CZRR dRdl 

= 16 X 3*3 

(iti) ^^V9*dl %*>%% 1 f!3> dildl. dt ^dt 3 

dT 1<d)l^ 3Td> f^RIdlRdT MldlMId^l SldlidRdR ddTH 

f^T. (^didtd R)HdM Wit dRITd I 3Id5 dRTld%) dld^d 
^ ft WIT fdoScT. 

ft WIT 3cTZ dvRRT RRT dl fdWd felfT. R’df 
dT ^ 3Rt W^i fddtddl ^tdRTtd %TTd. 

(3T) + \6 + = V* + + 61 + 3d = 

(d) ^3’ + 16* + + * t v’ = = H*’ + 

U'teMMl Wl-dRlft ^3 



3Tff&T, 3«rat «IT^ = n^ + van + ^s< + = UW 

3^ c hh<^<i^i 3 rtt 3^t ^5t ^t 

$*VsX ^ 3 RfM| 3T?1tw f^T TSTT^T f^qRf^TT f^TR ^TcTT 

?Rt cKdlR <-cHi 3TFPR ^RteT JRfrfer Mrferll ?R 
^^V^XX^^} ^ 37Tfnr ^ (3T) ^ (W) ^f^JT 
^3, — ' XK; RX, —3$ R1R ^ferr dddjt)HH" ^cM RRl'il RITRt 
f^i^T RfelT ^141 c^Ih J |<ild ^eidl %% 6 R ^C\o^ 

^fef. HT? T^uld feldl’^ll felR R 3RcIT RT TWIT 
^TF^TT ^ 3T^t Rls^e) c^R RR d>*M 3TWR l(Fddl sfer 3TRT 
H) 06 Pistil cl dMd>Hl M^dlcAH R^ 


3* Ref Mil'll] ^ fnooqui 

3<d<±-R^TT-3tf<i-«}(|M| RT A|]#fe U,<aic(] i?IT Ifer RR RRRTRT 

RHll % 3Rl ftaicidl %M, ^ Rim^Hl T3RI 3 flg<u | H 
RU^deT 3TT%. 




t\ WIT t3RT HfelT ^¥. 

t tfrI % 


3p5 WIT 3eI3 5FIRT 

TTFTlI 3 

^V9o^o^o<^^V9 

^TNfchl 

i rfel ? 
wf X 

\3^^o^o<^oV9^ 

Hldfi 'i Tftjld RRs^dl 3d3^Rr 
^<N W\o$ ^ fHodle). 

33T. ? : 


?l WIT ^31. 

t trrI % 


^ R^rr 3eI3 SRT 

wl ^ 



^tfrI ? 


HnO ^^fT 5cicil 

Rfe X : 


tn4 vjfPTt 


vsx 


7 JfuidH<) Rtfqfe 


X. -fi^feRT JJU||<*»KleUcvH JJUHebK ^rawt 

flW, x 6^ = V9XR^ W 

3RRT RT 3<J||chR|^l RTJR, ‘yRRi 3T#T 3rR RTcT ^oSWTRRI 3TTRI 
R 3^ 3feair R^f 33^ felT 3rfRRi % R o RTeJR R% R^R, R^RR R 
rRTRTfRFR RRIchkM 3RT RR^R TRfcT RfelT Wl. R?T : 

3JT>RTR, x XU = RXRU 


WT ^ R l 
T3^T Ifer 

3RRT T?|R rUI 
RfeT %3RT 


U<UxSXo*<U=^oX<U<UU 

I^oo % X <UXo o UU 

= <U^° oK^Ho o UU 


cb]um3l wit fell % R '3JR qRRel ?l dxxiu^iyicj] 3 ^ RR5R5 

3nt?T. ciHcbHl rrM Mr! rtrt R^dioii srtri r snwl sm 

WIT ^IcRIR. U-U RTeH Olefini RT <?Mt-edl ^^ld diinfeHl # 

fcrTR fnaHeil! 




W3^ J iMdl-^1Hdl 







# tnmictui'oqi nf5>«hi 4 »>»|«h 4) 

'd'ldld CT8J tRURWIdl cf RRTRT fRRRfRRRf <=h<u ijic^Rcll 

3TVj|yct,i^<s RWTR rlfcbcbl tR?RT 3TT%?T. rRT^Rit Rilft 

WRRTT fR rijr 3h^m 1 g<uii< grit. 

%. 3h30«j| ^tiftcT ST^shRM tuil^l X ^TT 3Tf RRI 3TfRRTRR WIT 
3TWR WT gift. 

•?. XH %% 3 ■Wld 3 R RTR RRRR Rk^I $1^1 R^H fRSfdelcrRI 
Wirat wrist (3WI!) WW RR:^fT t^RKT 

iSJ'bdld ftt. 

3- *RT l i u lf c bl WstRT RtRR o 03 ftcTt 3 #rf fjfWT 3TRirRt ttR, X, 
?H, Rid I 3Tlt, ft WsRT. 3TRTt IRR 1 ^ WsRT 

3frsnii41 rrM RimWinl feft sni ?RMidd w. r;. tr. 

RTRt 3T?ft WIT %o" % RTfTR 3RTRlt W I ft RRltRt 

W^I d-ut. % R Ridl % R t§TT IM 3Rtt ■H<sdi'»HldNdld ft 

RTflt, 3RI RFR 3TTRcT RR HRRd. ' 

X. RR dil u lrdl^1 N WNl RtRR o (RjWfR) R ffcT 3WIT cR N 
3lfRR> N RRT 3IdiMl ttR 3lfRRi ^ ft fHoSduil RiR^T 
WIT fast. R1R RRT WMl RtRRt ftft FTTRTR RJW 3TRRT ^ 
tcTTR ?RT WIRT ft RRTtzt RTF£ W Rift. 


• STTWff dVliV I Nl 3HT3Rff (WRRW^ 3TTO flRFlfTR tfWRc4[) 

+1 Marini ‘wwff <?iRiN't stir^r’ i rwirt ftR mi RiRelci 

3Rp t UH° w# jfe ^M'4f RRdldd RRt cR M^lld^l RT 
[dddlcR Tl^Ift ^RTR> fRRTef Riff. RT fRRRTRT Wtel 3TWRT RTR^T, 
cRRRT 3TTRtRTRTRT RTtR tsiR RT HdPdffidld RTIRtRRTRT t tWRlt 
fRoRRt t WT R>i)RRi RT fR:WRTRWR ^fclW HWTt 3R^R. fJT 
^d RR R tcT RTtRRRT RRRtR RRR RWlft R§fRR RdK'ddi ^RRt 
RilRRT %cTTcT. 

RT ^rdd>|-<RI 3TWTTRT WRRTR ^StcWRm RftRR Ri^R ^3J. 

\. HR RtRR ^>II-RT WIT RRSR, ? ^ R^fcfRT WTSRT fRRR 
WlMl SJRWRTT5RT RTTRRf RRlTRIRt RT ^Wdild RitSRi RfRR 
%^cft STT^rf. RT^f^Ri R^RT RTfuftf WTTRTRRtRT RRTRT R|RtRT 
RRRtR ftft. 

twit WIWRT oRWid.iRT RRoRRRt WlHt fRfW RRRT fR 
fR^eTt 3Tlt. 

\6 3?Rtt chldldRt ^IMI WWTT R>T?RTft RfttR 

RRjnfefWT RRfRRlRRT RileTIRRtWT trtRfcTt J^d^Rdd) TTRR 
dtHd^ct 3TT^R. 

X. RRcTTRRt WsRTR 3TdddtRTWT %tef 3TT%. 

^IdlpH 3RRR 3RRRf 3R ^H^vJ|H u i ^IR RT^ 3RTT ^ t 
tpfrRRI RlfRRRR Witt cRWRT 3RRRf 3RRtRRTf ^tgRT fttelt 
3TT|r. 

nrln< fRfRR RfJRfRirWT RWRTWRT RR^RfRI RRft iJRt, Rilft 
RRtR, TISRSRRRI 3TRTI 3TRRfRftR RTff#RT TlRlHM RT 

^•WRild RRTfRR %RfaT 3ft. g^R W^lt fIT ^WRil'd fR^RR 
fRRR WWFRRT ^eRT 3T^R ^ RTRStR# d^ldMI 3RRRT 

%^cRT dlddiMl 3TTRtRRTR RftcT, 3TW 3RT%. 





^ch)4] -ciicjuj] ?n 

37TfK^T^T Sf^ITT WTT *T?R r^T TFIcodl WTRjt ip ^T 3Tf«RT ^5T 
tffW 3vFT <dTKld RT? TTTsR q>l®e)<dl 3TF%. f^lNd: pDMI qTlft 
4 WhMI TITTT WM -qT^Jifl- 3TT%. Rp 

RP3f : 


%. 4ft WTftRTTW «h)nPi=h'H RRt <^4t ^H^ldls^) ^ ^cjl<l 

1%^ W fteT jfftft. 4q?T ^frwM =bN}=M]d) %%, V9^ 

3TTf&T Hoo | 3TR5t TRftf ftSR cR^TT TeftflcT ?cR 

4l|q*qR sNi x x x xfl 'jji^-cii cRTK c*JT 3M^JMl 
3 3 pRpklooqi Jl^ft tffar 3RR <a cfiReft 37T%. ‘fl 
WI^fT RftTT Rift RT?’ 3TTTT qpftRTHt %RftFPT 5PR %cTT 
3Tlt. 

9. dd< cqwl %<^RTT dft'Hi'1=b] RfT ^ftPFT Rr^TsT RRT 3TRY3R 
3TTt ft ^u|ft (3T) eRfft t T. R^JT ^oqr 

q|®fcq*il wti Rfamt, 

6$ 3[ft RR 3ffRi Ff?RTT TFtcF ftjR Hx^ \6^\ 4<ftd l 
ftftr? cRTR 3RR TRR R?NHi R5R %eff, ftcR 3 T Rm i fft| 
Rftlft <441 ^mq^i-cqi J ifuid1 ^smsIcii RT: 1 ^^ 3TU)fldf< fft?TT! 
0*0 ^3 rir rtf? ^t mw. ? r ^ p ra^dld 

^THt Vx q1< , H q><M rqi-ql sftta '5ft ^ ^ 3TTFFt fftgt TPIdl 

TTTdft 'Wld’^^IH Tp #5R ftt RTRt xjCF ?TlcTT. 

R ftt^t RFfddl RTR <£ % ftftt. fR# FIR Wf 3#. ft#3T } o 


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it. 'nrat mhjvmk) ^i^di #ttt : ^ awtwr ?r f^rr 

RTcik Wld^ -doidfi^ 3FFnt ^IrHI FT^t TpJF 

R5rt %etT ^rrat. mwzfi r 3tr^r m 
^iwtrr f^?k ?tcT. cR FflRRl^t 'Jl-H^IdKl %T 
R RcjyN’ SIFToS ^pp #f ^Rdldlel 3T^R TR^IT, 
^ra5t anf&T ^ rr TTRRRt w *rk ^Rtfmt an^Meft 
qi^uqmicil fsrf^f q)i4?hH 3TTQ^ ?t4. 1M 4. jhk RRfrnwn 

aTM^NR FFRiR, ‘ 7 ri4t Hc^K’ <l J INl RHT qj^d 3TTFRIT 
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cRft^r 4t diN^iidl, 3TNRTT dfuidl dil^ledn' qilBell. Wffei 
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^T^FT ^TTT TRcTT. ^TtcT Tl4 WrMt 4#3T : o^-^o-^- 
^ % = \o o '4^', I? H^FT c blH<q5<i'^qN ^IMId 3TTcT, STtf^T RT 
^FFft W>i d-H^ldl<t ^fkR T^T J lfuidMI FFRTFT 7 PMfaT 


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coR ^ ^ TRiR 4ell clft eft 






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pfftrT ^3teWRM * x 'iRT ^T^fT ^TfcXT R?TT 3#. 



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WT -d1<yiW 4RMKi J> ld 'dl^dRf \ 3Tra5T 3fl<rldl 

TTTjft. *^dd ?R RRTT xjy f^RWRT STT^JTW ^ 3T!^R. ^IT 
^ 3T^rat * TFTT, X XXR, 3 f^=Ff *IM ° ’MXlclHl Md+Nl txfa 
^ ^cR. W STTtrR^t ^X to5T $mt */* Mddiidl 
3TOTTT ^T ^RTT ^TF^fT T3°pT W Wt ft txfa fac6c|dl ^t. ^ 
^t XRft SRlt efRRT *t?t : 

'j^IdKt Xildldcr^f *f 1I T^ 3 ° ° <^ ; RT 3 o 3#T XfRT Jju||=blX 
^o K ^ = %oo (i) 

SflfbT c^TR ^ o 3#rj ^^t itxlR *RT f^TT^RT ftosqdl fX 
3 o + l\ + ^ = *3 (ii) 

.’. (i) + (ii) = 'Jll<j^l qlxxlld <t u lix) ^xl'd. 


XRlf 

X- 

X. 

?. 

x. 

H. 

V3. 


srFT XT. 4 .nU< Trfxrat X'O-X-X^h 

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^ RMfe^xRxf axxillx^n. ^fe^ir 3 ° ^nxf x^, x 

T^. ^JX 


C. =t>nA=bX 'ifuidl^ fag - xp ^TlfifR (Rr. R. XI?M) 

'X. W 'ifuidMl - ft. f. 'kr^lchX 
x ° . J i(“id*nxr - jit. xr. ’ll. Tftftt xsii^mx+x, "nfar. 






diiqUx *RTCRTR| rt^it gtxxr
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